If you take a quick look at that last post you will find a few simple measurements that demonstrate that CO2 and other “greenhouse” gases have an effect at the earth’s surface.

What Effect?

In brief, simply that CO2 and other greenhouse gases add a “radiative forcing” to the earth’s surface. A “radiative forcing” means more energy and, therefore, heating at the earth’s surface. And more CO2 will increase this slightly.

At this stage, we have said nothing about feedback effects or even the end of the world.. The series on CO2 is simply to unravel its effect on global temperatures all other things being equal. Which of course, they are not! But we have to start somewhere.

Here are two graphics from Part Six showing energy up and energy down that are the basis for many many questions..

The simple story these two graphics outline is that the earth radiates “longwave radiation” from its surface (because it has been heated by “shortwave radiation” from the sun).

The radiation from the earth’s surface is a lot more than the radiation leaving the atmosphere. Where does it go?

And why do we measure longwave radiation downwards at the earth’s surface. Where does that come from? And why do the wavelengths match those of CO2, methane and so on?

The answer – CO2 and other “greenhouse” gases absorb longwave radiation and re-emit radiation, both up (which continues on its journey out of the atmosphere) and down. The downward component increases the temperature at the earth’s surface.

The story sparked many questions on other blogs..

Questions like these are great, they clarify for me the common problems people have in understanding the “greenhouse” effect (always in quotes because it’s not really like a greenhouse at all!)

I’m not writing to try and change people’s minds. I’m writing for people who are asking questions and want to understand the subject. The only two things I ask:

Be prepared to think it over

If you have questions or comments, please ask these questions or make these comments (just remember the etiquette)

1. The Downwards Radiation is probably from the Sun

One commenter said:

You cite measurements of downward radiation. Were those measurements taken during the day or at night? Your link doesn’t say, and the answer is extremely critical to your argument.

I wasn’t clear why it really mattered so I asked. The response from the commenter was:

More than half of what we receive from the sun is already in the IR, so a daytime measurement is just measuring spectral lines by shining a light source through a gas. Anyone could do that in a lab with just air. The energy measured is just solar energy.

Anyone who has read the CO2 series on this blog, even just Part One, will have their hands in the air already..

Log plot of solar radiation vs terrestrial radiation by wavelength. The solar radiation is amount absorbed (i.e. takes into account typical albedo) and received at 45°.

Linear plot of the same data.

99% of the sun’s radiation has a wavelength less than 4μm

99.9% of the earth’s radiation has a wavelength greater than 4μm

There is almost no overlap, so if we measure what we conventionally call longwave radiation (>4μm) we know it comes from the earth. And if we measure what we conventionally call shortwave radiation (<4μm) we know if comes from the sun.

This simple fact is an amazing help in understanding the climate! But most people don’t know it!

Two related points have arisen, one of which is alluded to in the question above:

1. “Half of the radiation from the sun is infra-red, therefore..”

True but a red-herring. Infra-red means longer wavelength than visible light. Greater than 0.7μm. Not greater than 4μm.

2. “The sun’s energy is way way higher, so even though only 1% of its energy is greater than 4μm this will still overwhelm the earth’s energy above 4μm.”

This is true when we look at the energy at its source, but only a two billionth of the sun’s total energy is received by the earth. Alternatively, considering the radiation per m² the solar radiation is reduced by a factor of 46,000 (as a result of the inverse square law) by the time it reaches the earth.

The total energy from the sun’s radiation (at the earth’s surface) is very similar to the total energy radiated from the earth. (Actually no surprise otherwise the earth would rapidly heat up!)

2. Energy has to Balance (at the Top of Atmosphere)

If you measure all the energy going in at TOA vs all the energy going out at TOA, you will find that they net to zero over time.

This is true. Everyone agrees. The “greenhouse” gas theory doesn’t make a claim that contradicts this well-established fact. In fact, it relies on it!

Let’s clarify the numbers because I gave the “clear sky” results in the graphic, but most of the time it’s cloudy and then the numbers are lower.

The average over the globe and over a year at the top of atmosphere for incoming and outgoing radiation is about 240W/m2. Strictly speaking it is incoming radiation absorbed, because about 30% of “incoming” is reflected by clouds and the earth’s surface. Check out the numbers in The Earth’s Energy Budget. This is all measured by satellites.

Note – what is very important about this is that the radiation in and out at the top of atmosphere balance. Down at the earth’s surface many other effects are going on – convection, latent heat (evaporation and condensation of water) as well as radiation. Energy in = Energy out is true everywhere that no heating or cooling is going on. But it’s not necessarily true that Radiation in = Radiation out at the surface or in the atmosphere, as other ways exist of losing or gaining energy. At the top of atmosphere there is no convection and no water vapor, so energy can only be moved by radiation.

Hopefully that makes sense. Read on..

3. The most popular – You are “Creating” Energy!

Since there is no NEW energy being put into the system, and the amount of energy being put in will, over the long term, equal exactly the amount of energy coming out, all you get at most is a short term fluctuation. If I am wrong, then you have invented perpetual motion.

This is a common theme and a recurring one. Many people think that the theory is effectively claiming that CO2 is creating energy.

You have a house without a roof. It has a heater on the floor and there aren’t any other sources of energy. The temperature being measured is around 10°C, it’s a bit chilly. Someone puts a roof on the house, what happens to the temperature? It goes up, maybe now it is 15°C.

No, it can’t have gone up. The roof doesn’t create energy so the temperature must still be 10°C!

Of course, no one reading this is confused. But when I gave that example I had people still trying to demonstrate that this analogy wasn’t valid.

Suppose there was no energy source. The roof – or insulation – wouldn’t create any heat.

True – and if the earth had no sun heating it, CO2 wouldn’t have any heating effect at the earth’s surface either.

What is the theory claiming for CO2?

It isn’t creating energy

It isn’t adding energy to the climate system

It is absorbing and re-emitting “energy”

So instead of all the radiation from the earth’s surface simply heading up and out of the top of atmosphere, instead, some proportion is being “redirected” back down to the earth’s surface.

Like a roof but different.

The point is, there is no violation of energy conservation or any other law of thermodynamics.

The longwave energy being re-emitted back down to the earth’s surface – as you can see in the 2nd graphic above – simply increases the surface temperature. It increases the surface temperature above what it would be if this effect didn’t exist. (Like a roof on a house).

4. Your Radiation Numbers are Wrong

Referring to my “Upwards longwave radiation from the surface of the earth is around 390W/m2.”

Nyet. At 0 C, radiance is about 320 watts/m2. At 30 C, its about 550 watts/m2. You can’t just average the numbers from low to high across the globe and get the right answer either. you get a curve with a peak or high about mid day, but you also get a curve with a peak at the equator as compared to the poles. The average between the lows and the highs is NOT the average of the curve.

This is a very good point and worth covering in a little detail.

How do we come up with the number 390W/m2 in the first place?

There is a relationship between temperature and radiation, which is very well established, known as the Stefan-Boltzman law. You can see it at the start of the maths section in Part One.

Energy radiated is proportional to the 4th power of (absolute) temperature

Yuck. Before you skip forward, here are some example numbers (I used the amazing and recommended spectralcalc.com).

-20°’C (253K) or -4°F – 232 W/m2

-10°C (263K) or 14°F- 271 W/m2

0°C (273K) or 32°F – 315 W/m2

10°C (283K) or 50°F – 364 W/m2

20°C (293K) or 68°F – 418 W/m2

30°C (303K) or 86°F – 477W/m2

So our commentor was correct as to the method. If you want to work out how much energy is radiated from the surface of the earth, you can’t just assume you can use the earth’s average annual global temperature (15°C) to get the average radiation of 390W/m2.

This is true because the relationship is non-linear – see how the radiation increases more and more for the same 10°C or 10K rise in temperature.

Luckily this work has already been done for us, it doesn’t actually change the result that much.

What’s very interesting about this number is that it is nowhere near 240W/m2 – that number would represent a temperature of -18°C (about 0°F).

So in fact, energy radiated upwards from the earth’s surface is a lot higher than energy radiated out of the top of atmosphere. What’s going on?

5. If your numbers are correct, which I doubt, the earth will ignite

I’m not going to go check your numbers but just consider what you are saying. Your claim is that 156 w/m2 is being retained as extra energy kept inside the atmosphere over the long term. If you are right the planet should ignite in a few days.

So, we saw that the energy out of the system – from the top of atmosphere – is only 240W/m2

And energy radiated up from the earth’s surface is 396W/m2. So if the claim is correct that this “missing energy” is re-radiated back down to the surface, then simple arithmetic demonstrates that the energy will keep “piling up” and the earth will ignite.

Obviously that won’t happen. QED, the theory or the measurements are wrong. The defence rests.

Except.. let’s look a bit closer. The measurements are right, of course. So in fact, anyone disputing the theory needs their own theory to explain the numbers..

If we add extra radiation to the surface of the earth what happens? Simple – it heats up. As the surface heats up it radiates more energy back out. So it keeps heating up until the energy being lost is balanced by the energy coming in.

The point at which the earth’s temperature will stop changing is the value at which the outgoing radiation from the top of the atmosphere is balanced by the sun’s incoming radiation absorbed.

Well, that’s why the earth’s temperature is not -18°C. With no greenhouse effect it would be.

If there was nothing absorbing the upwards longwave radiation, and re-radiating some of it downwards, the radiation from the surface of the earth would only be 240W/m2 – a surface temperature of around -18°C (0°F).

Conclusion

To many people it seems like a wacky theory easily refuted by common sense, the basic laws of thermodynamics or the fact that the earth hasn’t apparently heated up for a decade. (I didn’t comment on that one, the climate is very complex, many factors affect climate).

The theory wasn’t invented by the IPCC or Al Gore (he only invented the internet). And it wasn’t formed from a desire to understand why the earth warmed up over much of the 20th century.

The theory was developed by physicists going back to the start of the 20th century (well, probably before but I’m haven’t studied the history of the subject). Thousands of physicists have studied the subject, dissected it, written papers on it and improved on it.

Even the many “skeptics” of what has become known as AGW in its IPCC form are not skeptics of these concepts. (e.g. Lindzen, Roy Spencer, John Christy)

I don’t want to try and pull the “argument from authority” because I don’t really accept it myself. But pause for thought if you are still not convinced, if you still think this theory magically creates energy from somewhere or violates the 2nd law of thermodynamics – and ask yourself:

If 99.99% of physicists past and present believe this effect is real and measurable, how likely is it that none of them realized there is a basic error in the theory?

Note 1

The value of 396W/m2 is calculated in Trenberth and Kiehl’s 2008 update to their 1997 paper: Earth’s Annual Global Mean Energy Budget. In the 2008 paper they comment that the upwards radiation from the surface cannot be assumed by averaging the temperature arithmetically and then calculating the radiation. So they take data on the surface temperature around the globe and re-calculate. Depending on exactly the method the values come in at 396.4, 396.1, 393.4. They stick with 396W/m2.

I’m (still) confused by the discrepancy of the out-going radiation at the surface vs. at TOA. I imagine a spherical shell at the surface where the energy flow is 396 Wm^2. Any other (concentric) shell should also have the total energy flow out, the same value ( ignore the difference introduced by the different radii of the shells…). It seems to my (muddled?) way of thinking that the energy is NOT being conserved … hence my confusion. Can you set me right?

Not muddled thinking, it is the first reaction on seeing the results. And the right question to ask.

Interesting that quite a few people have been telling me it’s not happening because it apparently violates various laws (other posts and other blogs).. but as it is happening – the measurements are straightforward – we need a theory to explain the results.

A theory that doesn’t set aside energy conservation, of course.

The energy flowing outward in this concentric shell gets absorbed (at certain wavelengths by certain gases). Some of it anyway.

Energy is re-emitted in all directions. As we consider a small vertical slice through the atmosphere we can think approximately here and say half of the absorbed radiation is emitted up and half is emitted down.

If there was no absorption in the atmosphere then the energy flowing upwards at TOA would be the same as the energy flowing upwards from the earth’s surface. Your thought experiment would be spot on.

But there is absorption. In Part Three where it got a bit technical I showed an equation which is central to mathematical solution of the problem which is essentially energy conservation:

It’s -18’C or 0’F at the surface. Upwards flux is 240W/m^2 from the surface. This is the radiation from a surface of -18’C.

And at the TOA, also 240W/m^2. This matches incoming solar energy absorbed. So all scientists are happy, except those who haven’t bought fur coats.

Now someone pours in a big vat of CO2 gas and swishes it around with a giant finger (so it’s well mixed). No one sees it of course, it’s invisible and the scientists are busy developing warmer coats.

What happens?

Some energy flowing upward from the surface is now absorbed by the CO2, and it is partly re-radiated back down to the surface which starts to heat up.

Less radiation makes it out of TOA, so there is now an energy imbalance. More energy in than out.

The planet heats up.

The temperature of the surface keeps heating up – causing great anger from the all the people whose livelihoods revolved around fur coats, and also from the scientists who initially can’t understand what is now happening to the energy flows.

The overall temperature keeps rising (and exactly how this energy is distributed is very difficult to calculate) but.. it keeps rising until energy flowing upwards at TOA matches incoming solar energy absorbed.

Your analogy is probably as close as you can get with this kind of analogy.

I really use the roof to try and show that increased heating at the surface without more energy from the sun doesn’t violate any thermodynamics laws. If a roof can do it, so can CO2.. so goes the analogy.

I couldn’t really find any good analogy for CO2 and other “greenhouse” gases because there is nothing in our experience quite like it (including roofs).

Exactly how more CO2 increases the temperature can be worked out mathematically – as explained in Part Five.

Although I haven’t shown all the results yet and will in a future post.

Near the surface as CO2 is doubled the absorption by CO2 is a lot less than double (see Part Four). But it’s complicated by the fact that higher up in the atmosphere there is less “saturation” of CO2 and this also has an effect.

Anyhow, you can’t just punch in the numbers on a calculator..

The current 1d numerical solutions to the physics equations – which probably won’t change much – produces a graph of increasing radiative forcing in W/m^2 as CO2 concentrations change.

The graph has a form where radiative forcing, with no feedbacks, is a log function of increasing CO2.

R = 5.35 x ln(C/C1) – where C is current CO2 level, and C1 is the pre-industrial level of 278ppm.

Sir Doom.
If you are going to pontificate in this manner, and quote others (I saw a few of mine in there) then do the right thing. I said on Watts Up With That that you could use some of what I said. That does not mean you can quote it out of context, present your own rebuttals while leaving mine out, and so on. If you want to give your readers a fair review, then post the links to the places from whence you got your comments so that your readers can see for themselves the while story rather than just your version of it.

I’m sorry. As is often the case with “out of context”, the person taking it out of context thinks he has captured the essence of it. I didn’t mean to cause offence or misrepresent your point of view.

So, how to fix it?

First, which comment or comments are the issue?

Second, I can
– link to the blog post it came from (but I don’t know how to link to a comment, so there will be 300 comments for readers to sort through)
– or you are free to provide a commentary in the responses here about what your point of view really is

Third, I could remove them – but the reason I chose them was they captured the essence of many points that many people have made, so I would want to express that point of view somehow.

Anyway, once again, my apologies and let me know how best to rectify the situation.

I like the balanced way you present your articles and comments. I wonder if you could answer or at least discuss a query I have regarding the effect of CO2?

Before that, I have replied to this comment because you state “I don’t know how to link to a comment…”. I think you’ll find that if you click on the date and time of each comment, the full link will be displayed in your address bar. I’m pretty sure that would work.

Here is my question:

What do you think is the contribution made by CO2 to the ‘Greenhouse Effect’?

I have a problem making sense of some of the high-percentage answers given by certain papers (eg Lacis, K&T), and would welcome the opportunity to hear your views.

The contribution from a doubling of CO2 is estimated to be about 3.7 W/m^2 of additional atmospheric absorption or reduction in the direct surface to space transmittance (i.e. the amount of surface LW flux that passes straight to space as if the atmosphere wasn’t even there).

Using K&T’s diagram, it appears they have either a 70 W/m^2 or 40 W/m^2 direct surface to space transmittance. Some people claim the additional 30 W/m^2 is the transmittance from the cloud tops to space rather than the from surface directly through the clouds to space. In any event, assuming the direct transmittance is 70 W/m^2, if CO2 is doubled this decreases to 66.3 W/m^2 (70-3.7 = 66.3) and the atmosphere absorbs an additional 3.7 W/m^2 that previously passed from the surface straight into the space.

If you want to think of the perturbation in terms of percentage, you could say that it increases atmospheric absorption by about 1.2% 3.7/320 = 0.012 (390-70 = 320 W/m^2 absorbed by the atmosphere). Or the total absorption increases from 320 W/m^2 to 323.7 W/m^2 when CO2 is doubled.

Thanks very much for your input. I agree the numbers from K&T are represented in your post but that doesn’t really answer the question “How much does CO2 contribute to the ‘GE’?’ Maybe I wasn’t clear enough.

In particular, I meant as a percentage of the GE in terms of temperature (although I appreciate the ‘GE’ can also be considered in terms of radiation balance). The ‘GE’ is considered to equate to 33 deg C (or K). How much of this is due to CO2? Trenberth considers it may be as much as 26%. Lacis says 20%. To me, these are gross overestimates. Using your figure of 1.2% increased absorption, a doubling of CO2 would only increase global temperature by 0.4 C. I appreciate this may be simplistic but I would like some clarification.

I don’t have time to follow yet another blog but I will tackle one of your points. Consider my comment that you quoted where I said an extra 156 w/m2 would ignite the planet. Of course it would not, I was exagerating to make a point, which was that your assumption that there was 156 w/m2 more power coming out of the earth surface than was coming out of the TOA was not realistic. Even the most wild eyed IPCC —–ists (moderator’s note, see Etiquette) are only claiming a net 1.4 w/m2 being recycled by CO2.

Your error continues to be your assumption, repeated here, that upward longwave radiation from earth surface and upward longwave radiation from TOA can be compared in a meaningfull way. Sorry, but what you need to compare is ALL wavelengths. Plenty of shortwave radiation goes up and out too, and it goes right through CO2 like it wasn’t there. If you want to calculate an energy balance between the two layers, you can’t just focus on one wavelength, you have to look at all the mechanisms that move energy and compare them. You can’t even limit your analysis to just radiated energy either, because a lot gets moved around by conductance and at sea surface a ton of energy moves into the atmosphere via evaporation (so the upward w/m2 number you are using for earth surface is actually LOW when you consider all ways to move energy around instead of just longwave).

Check out Earth Radiation Budget Experiment (ERBE) which are satellites NASA has up in orbit that monitor incoming and outgoing radiation at a broad range of wavelengths across earth surface. One of the things they show is that the earth gains energy at the equator (where its radiance to space is highest) and loses it at the arctic zones (where radiance to space is lowest). The net across all wavelengths however is no where near 156 w/m2. Go check out AMSU-A which measures temperature at many different levels of the atmosphere. You will find that the layers with CO2 in them (the lower ones) oscillate in tandem with land mass, but opposite from sea surface which is 3/4 of the planet.

At TOA, as measured by satellite – incoming radiation from the sun that is not reflected is about 240W/m^2 – when we average it across the whole surface of earth. (See Earth’s Energy Budget for full explanation)

At TOA as measured by satellite – outgoing longwave radiation from the earth is about 240W/m^2 – averaged globally and annually.

Energy balance across all wavelengths. Energy in = energy out at the top of atmosphere. We all agree, I believe, on this point!

The problem many people have is visualizing how it could be possible that on average396W/m^2 of longwave radiation leaves the surface of the earth and on average only 240W/m^2 leaves at the top of atmosphere. (These numbers take into account the huge variations from equator to poles).

It seems like a huge mistake. “He must be crazy!”

And yet both can be measured. The longwave leaving the earth’s surface cannot be measured by satellite of course.

And if only 240W/m^2 of longwave radiation was generated from the earth’s surface that would mean an average temperature of -15’C. (Stefan-Boltzman law)

Commenting on a few quotes:

Even the most wild eyed IPCC —-ists are only claiming a net 1.4 w/m2 being recycled by CO2.

Roughly correct, but let’s get the “number” into the right context. The “radiative forcing” at TOA of current levels of CO2 compared with pre-industrial levels is calculated as 1.7W/m^2 (see Part Seven).

The calculation of “radiative forcing” is simply the difference from where we were in 1860 or 1750 and where we are today. (Even that number is not necessarily an “imbalance”. If the climate system has heated up to equilibrium as a result of this small increase, at TOA energy in= energy out).

This is a totally different parameter from upwards and downwards flux at each height through the atmosphere.

The working measurements of flux levels upwards and downwards at different heights is not usually shown in IPCC literature – you just see the results. But it is in atmospheric physics text books and climate papers.

That’s the reason for showing it. Most people haven’t seen it. The reaction is surprise because it takes a while to realize that energy is not being created, or stockpiled, just absorbed and re-radiated back down.. “the only explanation”

Your error continues to be your assumption, repeated here, that upward longwave radiation from earth surface and upward longwave radiation from TOA can be compared in a meaningfull way. Sorry, but what you need to compare is ALL wavelengths. Plenty of shortwave radiation goes up and out too, and it goes right through CO2 like it wasn’t there..

The TOA calculation for incoming solar (shortwave) radiation absorbed already takes into account solar radiation reflected from the earth’s surface. So the shortwave radiation that is reflected from clouds, aerosols in the atmosphere and the earth’s surface does not need to be included – because it doesn’t get absorbed anywhere.
And you are correct, shortwave goes straight through CO2 (almost-for any purists reading this).

The simple point is – longwave radiation leaves the earth at about 396 W/m^2.
And at the top of atmosphere at about 239 W/m^2.
They are the averages, so how the energy is redistributed from equator to poles doesn’t affect this.

These can both be measured.

And shortwave radiation reflected from the earth’s surface doesn’t impact on these measurements. (On the other hand, shortwave radiation that is absorbed by the earth’s surface is what heats the surface up, and consequently it radiates out longwave)

How to move forward for those still doubting my numbers or my sanity?

Feel free to ask questions, of course. Absorbing this concept is not “intuitive”. Most of physics is not intuitive until the concepts have become familiar.

But another more interesting way if you think I am wrong– add your comment with the following information and you can be approximate, we aren’t going to be picky about 5 W/m^2 here or there:

1. It seems you now agree that total energy flux is the correct measurement, not the one you presented.
2. The numbers you quote above are approximations based on various theories. These are not the data being produced by measurements such as ERBE.
3. An analysis of the ERBE trend data shows a slope EXACTLY OPPOSITE that predicted by the IPCC climate models. You can see ERBE data plotted against the predictions of 11 IPCC climate models on page 4 of this paper: http://scienceandpublicpolicy.org/images/stories/papers/originals/co2_report_july_09.pdf and see that they ALL got it wrong.
4. Superimposing CO2 increases measured since 1960 (and extrapolated backward according to IPCC estimates) show global temperature from NASA/GISS increased before and after rise of CO2 in roughly the same progression, and a cooling trend has set in at just the time the climate models predicted CO2 forcing would be causing exponential temperature increases. http://knowledgedrift.files.wordpress.com/2010/01/temp-vs-c02-long-term1.png

So… neither the ACTUAL MEASUREMENTS of the earth energy budget, nor the ACTUAL MEASUREMENTS of the earth surface temperature provide any evidence that CO2 is significant to either. The climate models which rely on the notion that it does, have all produced predictions that are increasingly wrong as we get more ACTUAL MEASUREMENTS to compare them to.

1. I’m just trying to find different ways to explain the same point. I just don’t think you understand what it is I’m trying to explain.

2. The numbers at top of atmosphere are from ERBE. The one number – upwards longwave radiation from the earth’s surface can’t be from ERBE because it can’t measure longwave radiation from the surface.

If you think the longwave radiation upwards from the earth’s surface is 240W/m^2 – why not say it?

There are probably 1000’s of papers which support Stefan Boltzmann’s law:
Energy per unit area per second = emissivity x 5.67×10^-8 x T^4, where T is in Kelvin, and emissivity is between 0 and 1.
These numbers have been measured and verified for over 100 years and are foundational for thermodynamics. The numbers for emissivity of the earth’s surface of all different types have been measured (very close to 1) and verified for decades.

Is Stefan-Boltzmann’s law wrong?

Our point of difference is definitely not that I am using “an approximation”. I say the average annual global upwards radiation from the earth surface = 396 W/m^2.

You haven’t come out and said what you believe the number is. But apparently, you think it should be “about 240W/m^2”.

You haven’t actually stated your number – but every time I point out the difference between the 2 numbers (longwave TOA and surface) you tell me:

a) your numbers are wrong, and/or
b) it can’t be right because this is a huge amount of energy to be going somewhere

The difference is not an approximation.

The difference is well explained by a theory that involves CO2, water vapor and other trace gases absorbing and re-emitting energy.

If you have an alternative – which I suspect you don’t – why not come up with your numbers for X and Y in the previous post?

3. There is no mention in this series about IPCC models (except in passing that they are not used to solve this problem).

It’s irrelevant.
Let’s solve one problem at a time.

What’s the best way to begin to understand the role of CO2 in the climate?

a) Jump into a debate about GCMs which tries to solve a massive computational problem involving 100s of equations and 1000s of boundary conditions?

You haven’t actually stated your number – but every time I point out the difference between the 2 numbers (longwave TOA and surface) you tell me:>>

I will tell you one more time. The 2 numbers are meaningless to the problem. You measure TOTAL flux in, by all mechanisms, at each layer, and compare to TOTAL flux out by all mechanisms, at each layer, to determine if energy is being retained and how much and where.

Stefan-Boltzman is in fact correct, never did I say it wasn’t, once again stop putting words in my mouth. There is no value in discussion if you are going to use those tactics. Your explanation of CO2 retaining energy is reasonably sound. The order of magnitude is miniscule.

I don’t think you’ll have much success educating David M Hoffer, who apparently believes that positive feedbacks can’t exceed negative feedbacks in earth’s climate system because it would violate the second law of thermodynamics, something that all the physicists working in the field have apparently missed …>>

They haven’t missed it. Several papers at the PhD level have been submitted by physicists. Rebuttals from climatologists have varied from calling them nonsense to ignoring them.

Doom,
Rather than debate you based on a false premise and which numbers mean what, I dropped this thread and instead wrote an explanation of what happens to longwave as it travels through the atmosphere on my blog. Sorry it took so long, but here it be.

The real question is, what temperature range produces an emission spectrum that most closely matches that 10 to 12 micron range where the window for photons to escape to space is pretty much wide open.

It’s a “nice analysis”, but to be sure we have it right there is no substitute for a little maths.

Let’s take a closer look at the energy under the curve using Planck’s law. This law is the mathematical formula for energy radiated vs wavelength. Then if we integrate between 2 wavelength values we can find the total energy in that part of the spectrum.

Note: The well-known Stefan-Boltzmann law is the integration across ALL wavelengths and works out to, j = e.sigma.T^4 (When it is a pure blackbody emissivity, e=1)

Now lets look at the energy in the 10-12um band. And let’s also look at the energy in the 8-12um band because apart from a small area of absorption by O3 (around 9.6um), this is also a significant part of the “atmospheric window”.

Let’s look at the proportion of total energy within these 2 bands for a number of temperatures:

1. The numbers aren’t correct. Even across the wide range of surface temperatures the energy radiated from those surfaces within the “atmospheric window” doesn’t change too much. This appears to be a blow to the analysis above.

2. The “hand-waving” analysis can sound interesting. But the only way to actually work out the real absorption and re-radiation is to solve the RTE (radiative transfer equations) in a vertical profile through the atmosphere. This needs a significant computational effort because it requires the absorption profile of every gas by wavelength. You can’t do it on a calculator without many years.

If you do it by qualitative discussion it has a low chance of being right. Like trying to work out the motions of Pluto with an abacus.

I have been reading this site for some days and think it’s one of the best for learning basics about GH effect and other similar subjects, thanks to ScienceOfDoom for this effort. I really think people who tell that CO2 can’t have any effect on climate should read this together with all comments.

What is the ScienceOfDoom’s take on this – which part of the theory can be wrong? We have not reduced our CO2 emissions, they are still rising but the oceans started to cool few years ago and looks like our climate system loses more energy than receives!

Clearly the climate is complex and some areas are not well understood. I hope to do some posts about some of these areas, especially clouds, which are described by the great Ramanathan as “the Gordian knot” of climate.

The contrast we were discussing was between the longwave radiation leaving TOA, and the longwave radiation leaving the surface.

The satellite can measure the longwave radiation leaving TOA. It can’t “see” the surface at those wavelengths – not to do an accurate measurement of longwave radiation – because the atmosphere absorbs at those wavelengths.

However, it’s very easy to measure and calculate the longwave radiation at the surface – from the Stefan-Boltzmann equation = emissivity x 5.67×10^-8 x T^4

Regarding measuring the LW leaving the earth–since the atmosphere absorbs at those wavelengths, is it even possible to directly measure it, or does it have to be calculated? I mean, how much atmosphere does it take to affect the reading? You could point the sensor at the ground from 6 inches away, but then are you yourself interfering by casting a shadow?

If I’m understanding your explanation correctly about the difference in LW leaving the earth’s surface vs SW incoming at TOA, the remaining 156 W/m^2 is “in-transit” in the atmosphere? Due to re-radiating back and forth between the layers, moving air masses, condensation, evaporation, etc.? And eventually, all of that would at some point either get radiated out to space, or it would radiate it back at the surface of the earth to be absorbed there. And that energy lost from the atmosphere either to space or back to the earth would then be “replaced” in due time from “new” LW surface radiation to keep the balance.

Is there an upper limit to the amount of energy that can be in transit in the atmosphere?

Regarding measuring the LW leaving the earth–since the atmosphere absorbs at those wavelengths, is it even possible to directly measure it, or does it have to be calculated?

It can definitely be measured, but it’s easier and cheaper to measure the temperature.

As you go further up in the atmosphere you get progressively more absorption and therefore you will measure less upwards radiation, and the losses will be concentrated in certain bands – like 15um for CO2 and 9.6um for O3.

Down at the ground level you can buy an instrument and leave it to log while you walk away. The radiation from a body at a given temperature is well known and has been so well validated over 100 years that it isn’t something that has any doubt around it.

Is there an upper limit to the amount of energy that can be in transit in the atmosphere?

It all depends on the mechanisms for absorption and reradiation in the atmosphere and the effectiveness of moving heat from the surface.

Let me give an example. Suppose something magically happened so that no heat was moved from the surface by evaporation of water (and condensation higher up in the atmosphere).

This would mean that there was less removal of heat from the surface – and so the surface would heat up until there was a new equilibrium between surface-atmosphere and atmosphere-space. Perhaps that might be an average surface temperature of 30’C instead of 15’C. This surface is now radiating at about 470W/m^2 instead of 390W/m^2.

Suppose someone “poured” massive quantities of CO2, CH4, O3, NO2.. into the atmosphere. Is there a limit? Probably at some point.

But you can see the effect of a change in this one process. The surface gets hotter and radiates more to balance.

At the surface all of the heat movements balance out to zero. At each level in the atmosphere the same. And at the top of atmosphere the same.

Forgive me but I do not have the time (and am a bit rusty) to do the math (which probably disqualifies my opinion right off the bat) but what I see on these (and all other) charts is that CO2 has an absorption bandwidth that is rather narrow and peaks rapidly where it is not matched by other gases. Does that not mean that CO2’s absorption of energy is inversely proportional to its concentration? Leading one to suppose that once you reach a certain point of CO2 in the atmosphere (or as a perfect gas) you would reach a maximum temperature for that specific influence?

“The radiation from the earth’s surface is a lot less than the radiation leaving the atmosphere. Where does it go?”

From the numbers you give, this appears to be an error and should read:
“The radiation from the earth’s surface is a lot MORE than the radiation leaving the atmosphere.”

Yes?

Thanks for your efforts to explain this stuff, and especially your tone and patience. Although you engage in some satire here and there, you do not seem to indulge in sarcasm directed to individuals. Most refreshing.

You’re welcome.
So, would it be correct to say that
1) under steady state conditions, the “black body” radiation temperature of the earth’s surface is such that the energy leaving the TOA is equal to that entering the TOA from the sun; and that
2) if additional energy-absorbing “greenhouse” gases are added to the atmosphere, thus perturbing the steady state, the re-radiation of that energy results in a new steady state with the surface radiation temperature raised to the level required to rebalance the incoming and outgoing energy at TOA?

So, would it be correct to say that
1) under steady state conditions, the “black body” radiation temperature of the earth’s surface is such that the energy leaving the TOA is equal to that entering the TOA from the sun..

The statement is compressed enough that it might be misunderstood. But yes.

..and that
2) if additional energy-absorbing “greenhouse” gases are added to the atmosphere, thus perturbing the steady state, the re-radiation of that energy results in a new steady state with the surface radiation temperature raised to the level required to rebalance the incoming and outgoing energy at TOA?

Earthshine, as you mentioned, is generated by the planet absorbing shortwave (higher energy), and releasing longwave(lower energy) radiation. This radiation, together with CO2 and H2O gas, creates the greenhouse effect. I agree. HOWEVER…
Did you take into account the oceans (71% of earth’s surface) absorbing solar energy? Blue light is scattered the most in seawater, and eventually reflects back. But almost all other wavelengths are absorbed! Of course, this makes sense, since oceans lose heat through evaporation, yet do not freeze, so there must be an energy input into them to balance things.
Therefore: shouldn’t earthshine’s spectrum be very minimal over salt water? That is, isn’t the greenhouse effect missing over the oceans? If this is true, then isn’t positive feedback called into question?

Thank you for this informative site. I have added it to my recommended sites at http://jcmooreonline.com/. The posts here are rather long and I’ve not read through all of them but I did not see a mention of the role of collision deactivation of vibrationally excited CO2 molecules. The primary processes is the absorption of a photon but the excited state may be deactivated by both radiation and collision . At STP, a collision with another molecule occurs about every 10 to -9 seconds while the radiative lifetime is about 10 to the -6 seconds, meaning a molecule would normally make about 1000 collisions while in the excited state. Collision deactivation would heat the atmosphere but it will not show up in IR radiation directed back to Earth. Is the rate of collision deactivation so small that it can be ignored?

Is the rate of collision deactivation so small that it can be ignored?

Exactly the opposite. The rate of collisional deactivation must be very much larger than radiative emission in order to have local thermal equilibrium and Kirchhoff’s Law (emissivity = absorptivity) apply. The emission rate is dependent only on the number of molecules in the excited state, not on the lifetime of an individual molecule in the excited state. The fraction of molecules in the excited state is determined by the Maxwell-Boltzmann distribution, which is a function of temperature only. For a more complete explanation you could read my post here:

Oh, and most collisions are elastic with no energy transferred. Only about 1 out of 1000 collisions results in energy transfer. So the lifetime of an excited molecule is more like 1 μs rather than 1 ns.

Firstly, I quite agree that the ‘Greenhouse Effect’ is inappropriately named, that is why I used single quotation marks.

The question is simple enough. I don’t have a theory and I certainly would not presume to “calculate the effect”! I tend to approach this problem from logic, not science. But I believe that science should at least make sense. I merely question the percentages given by Trenberth and Lacis, so I asked what you think the contribution is. I will, however, expand on my problem with their figures…

Lets take Lacis’ 20% of ‘GE’ is due to CO2:
20% of 33 C is 6.6 C.

In 1850 (the start of IPCC’s ‘accurate data’) the CO2 concentration in the atmosphere was 0.028%. The global temperature was appx 0.9 C lower than today (due to the ‘enhanced GE’ today), source HadCRUt.

Today we have had an appx 40% increase in CO2 with a contemporaneous (but not necessarily caused by) rise of 0.9 C. Today’s ‘GE’ being 33 C.

Therefore, the ‘GE’ in 1850 was 32.1 C. 20% of 32.1 = 6.42 C.

Therefore, Lacis is postulating that a trace gas which caused 6.42 C of the ‘GE’ in 1850, having been increased by a significant 40%, is now contributing 6.6 C to the ‘GE’. This is a rise of 0.18 C. This seems an anomaly. If CO2 makes a significant contribution (20%) to the ‘GE’, why has here not been a significantly greater warming than has been observed?

“Thanks very much for your input. I agree the numbers from K&T are represented in your post but that doesn’t really answer the question “How much does CO2 contribute to the ‘GE’?’ Maybe I wasn’t clear enough.

In particular, I meant as a percentage of the GE in terms of temperature (although I appreciate the ‘GE’ can also be considered in terms of radiation balance). The ‘GE’ is considered to equate to 33 deg C (or K). How much of this is due to CO2? Trenberth considers it may be as much as 26%. Lacis says 20%. To me, these are gross overestimates. Using your figure of 1.2% increased absorption, a doubling of CO2 would only increase global temperature by 0.4 C. I appreciate this may be simplistic but I would like some clarification.”

This is a difficult question to answer definitively or accurately because there are arguably multiple ways to quantify the total contribution CO2 has on the GHE.

In general though, about a little less than 1/3rd of the absorption spectrum is from CO2 and other GHGs and the remaining 2/3rds or more is from H2O. Where it gets complicated is quantifying the net effects of clouds in combination with the H2O overlap in the CO2 absorbing bands. In general, anywhere that is cloud covered, CO2 and other GHG absorption would matter little because the clouds would be absorbing the surface emitted energy anyway. Clouds cover about 2/3rds of the Earth’s surface.

You could estimate that CO2 absorption could be reduced by about 2/3rds as a result of the presence of clouds – making its total contribution only about 10% rather than about 30%. There is also the issue of water vapor overlap in the CO2 absorbing bands – meaning in the absence of CO2, water vapor would still absorb some of what CO2 absorbs anyway. How much is hard to know.

I think it’s accurate to say that about 90% or more of the GHE is from H2O in the form of water vapor and clouds) and about 10% or so is from CO2 and other GHGs.

Thanks for the comment. Please see my reply to SoD above regarding my doubting of the 20-26% figures given by Trenberth and Lacis.

I have to say that, intuitively, I mostly agree with your estimate of 10% contribution by CO2. In fact, I believe that observed data actually tends to support a slightly lower percentage but the exact amount cannot be quantified until someone figures out how much of the observed warming since 1850 (date chosen as being the start of IPCC accurate data, although the IPCC states anthropogenic warming started in 1750) is specifically due to CO2. I suspect that 5-10% is a more pragmatic figure.

Thanks for your explanation. I see where your conceptual problems lie.

1. The assumption that increases in CO2 are responsible for the complete temperature change over the last 150 years.

I expect that you are using it as the working hypothesis of others. However, I don’t know if anyone claims that the radiative forcing from CO2 is and is alone responsible for the approximate 1’C warming of the last 150 years.

There may be scientists with good credentials who say it (let me know) but I find it difficult to take it as a proposition with a scientific basis given the wide fluctuation in temperatures over the last million years.

2. The assumption that there is a linear relationship between increases in CO2 and temperature change.

This is definitely not in any textbooks. In fact, there is definitely not a linear relationship between CO2 increases and radiative forcing so it seems impossible for there to be a linear relationship between CO2 increases and temperature changes.

3. The assumption that current temperatures reflect the complete effect of any CO2 changes.

There is a high level of thermal inertia in the climate system. Even without the complexity of natural variation and feedbacks, the temperature today will not be a reflection of the radiative forcing today.

In summary what you are trying to find is a relationship between the temperature change (up to this year) and the effectiveness of CO2 (given its concentration this year) using linear relationships as the basis. This approach has no chance of working.

a) the spectroscopic measured strength of the few 100,000 lines of CO2
b) the spectroscopic measured strength of the many lines of H2O (can’t lay my hands on the number of lines right now)
c) as a) and b) for other radiatively-active gases
d) the estimated strength of the water vapor continuum from experimental work
e) the solution to the radiative transfer equations given various temperature profiles of the atmosphere and concentration of these gases
f) the solution with each gas in turn removed

Each item a) through f) is well understood with the exception of d) which is still well characterized, but lacks the theoretical basis of the other items.

This means that the effectiveness of CO2 vs water vapor can be calculated with scientific confidence in the result. It is theory that comes from fundamental physics backed up by experiment.

If we had to work from global temperature change to assess the “greenhouse” effect and the relative effectiveness of the different gases I expect that the science of radiative physics would not have made much progress over the last 100 years.

First of all, thank you for your detailed and fairly comprehensive reply. You do, however, make certain assumptions about my ‘conceptual problems’ which I would like to clarify.

Secondly, and equally importantly, you have not yet answered my original question: “What is the contribution made by CO2 to the ‘GE’?”

To the question: At some point all the ‘basic theory’ you speak of should be validated or falsified by observed data. All I am trying to gauge is what proportion of the GE in terms of temperature is due to CO2. Following from that, I can then seek clarification on the other non-condensing GHGs which, although far less abundant, are seemingly given a significant part to play according to Lacis and Trenberth.

I am trying to understand these claims and to make sense of them. That’s it. Why? Because before anyone can start talking about ‘catastrophic anthropogenic global warming’ they really need to establish that they know – pretty accurately – what the current (and historic) contributions are. I would appreciate your answer.

So to my ‘conceptual problems’:

1. I most certainly do not assume that CO2 is responsible for the complete warming over the last 150 years. I am unsure why you would even suspect such a thing. I even stated in my previous reply that the warming was “contemporaneous with but not necessarily caused by” the increase in CO2. To take this important point further, all anyone can say is that CO2 may or may not have contributed an unknown proportion of the observed warming’.

2. I do not assume a linear relationship between CO2 and temperature, but I do appreciate why you might have thought this. Hopefully you can clarify what the relationship is (log?) but the fact remains that the cAGW scare was sold on an ‘accelerating’ effect of the warming due to CO2. Therefore, my implied use of a linear relationship is actually a less severe relationship than that which has been ‘advertised’. This is where I disagree with your assessment of my ‘problems’. If they are problems, they are problems of mis-selling the wrong initial basis. To put it bluntly, in 1998 I (Joe Public) was sold a ‘mankind is going to cause a runaway catastrophic warming due to his continuing and accelerating emissions of CO2 et al’ bill of scientific goods. The MBH98 graph showed a fabulous hockey stick shape and ‘implied’ a steepening gradient. It was as simple as that. I therefore approach this debate from the point of view of layman, albeit one who largely understands scientific concepts, particularly in the atmosphere.

My original question is still a valid one. If Lacis & Trenberth (& Schmidt etc) are right, why hasn’t the observed warming since 1850 been relatively commensurate with the significant increase of a ghg to which they have attributed a very significant contribution? Which brings me to your point 3…

3. Thermal inertia. The problem with this argument is twofold (maybe more):

a. No evidence
b. No logic in the context of the cAGW debate.

No evidence because any ‘lag’ effect, however large or small, has had a significant period to have shown up in observations. The IPCC states that anthro-effects commenced around 1750. Accurate data started in 1850. Even if you ignore the 1750-1850 period, this means the ‘radiative effect’ of CO2 has had over 150 years to produce some sign of its ‘lagged’ existence. As we both agree that the entire 0.9 C warming cannot be solely due to CO2, this means that ‘some’ of any observed effect of CO2 is due to ‘lag’. Any assertion that 150 years is not enough lag needs to be backed up with a reference and, ideally, evidence. Furthermore, any ‘lag’ will have a cumulative effect (agree?) and therefore the warming ‘due’ to CO2 should be accelerating (adding to the non-linear effect). There is absolutely no evidence to support this assertion. Even with natural variations and feedbacks, the temperature of today must include a portion of ‘inertia’. Logically, if any natural variations have the ability to not only combat the radiative effect of CO2 but also the ‘lagged’ effect of the same, then how do we know that any of the 0.9 C warming is due to CO2? (I do accept the idea that there must be some effect, however small!)

My approach may or may not have ‘no chance of working’ but the basic theory of radiative forced warming has had ample opportunity to work with no definitive result.

Reading your links, you assert a 1 deg C ‘no feedback’ sensitivity for CO2. I don’t have a huge problem with that figure except that the observed rise so far includes all feedbacks and forcings. If the relationship between CO2 and temperature is indeed non-linear, does this mean you would expect a lesser warming for the next 40% increase than the ‘unknown portion of 0.9 C’ we have witnessed thus far?

Do you see now why I am so keen to respectfully request your answer to my original question? I value and appreciate your engagement on this.

Re your second point – that CO2 does not produce a linear response in the climate.

Temperature can only increase, stay neutral, or decrease with added CO2.

Considering that CO2 only affects a narrow bandwidth of IR and that this bandwidth is pretty much saturated for IR blocking it suggests that the actual effect of increasing CO2 produces a declining influence on temperature. This was shown back in the 1800s with the first IR experiments with CO and CO2 and substantiated subsequently – why this fact is overlooked (ignored) now escapes me…

I’m not sure if you are replying to me or SoD. It was his second point originally.

I understand your concern. If, the relevant bandwidth is indeed saturated or nearly saturated, then an increase in CO2 would have a decreasing effect on gt. This does seem at odds with the IPCC forecast of ‘accelerating change’. The lack of further warming since 1998 would lend credence to the idea of declining influence but 13/14 years is still a fairly short period to discount further anthropogenic effect from CO2.

I haven’t yet answered your original question. I need to review some papers to do that. However, I understand the principles they use and I agree with the principles.

That’s why I explained the principles first, because if you don’t understand the approach then the result won’t be of benefit.

Apologies if I have misunderstood your premises and working assumptions.

But we are still poles apart as far as method and approach is concerned. You appear to be trying to ascertain CO2’s contribution to the total “greenhouse” effect via temperature changes over recent history.

As far as “stuff people have done” in “selling AGW” etc, I am not particularly interested. Other blogs are much better places for those discussions. If something is textbooks physics then that is a good starting point. If you want to take a different tack as to what the physics “should be” because of PR tactics or whatever I have already lost interest.

I am saying that CO2’s contribution can be calculated via fundamental physics. This is well proven via experiment as shown in one of the links already provided.

I am also saying that there is little chance of finding CO2’s contribution to the total “greenhouse” effect via temperature changes over recent history because climate is very complex.

If you think that items a) through e) in my original list are unproven in any way I will be happy to address them.

If you think a) through e) followed by f) doesn’t build a case for the total contribution of CO2 to the “greenhouse” effect I would like to hear your explanation as to why.

I am truly sorry you have already lost interest. My point regarding the ‘selling’ was not meant to be a political one. It was an answer to your assertion that I had ‘conceptual problems’. If the physics was correlating with the evidence, then maybe I would not consider that the selling was incorrect.

I would genuinely prefer if you could answer the question, and then proceed to try to equate your answer with the principles as you describe. However, you are still making assumptions about either my motives or my methods. When you state that ‘[I] appear to be trying to ascertain…’ you are making an incorrect assumption.

I repeat I am just trying to rationalise the large percentages (of ‘GE’) attributed to CO2 by papers such as Lacis and Trenberth with the following logic:

If the fundamental ‘physics’ is so clear, how can 0.028% of the atmosphere cause such a significant portion of the 32.1 C ‘GE’ in 1850, yet a 40% increase of said trace gas only produce an (as yet unknown) portion of a relatively tiny warming of 0.9 C?

This is a fundamental anomaly. I have explained why “thermal inertia’ does not adequately address the anomaly. Your links provide much information about radiation, but not about heat. If your explanations truly can explain CO2’s contribution via experiment, then please explain why the observed evidence does not obviously support the theory.

None of the items in your list relate to actual temperature increases due to radiative forcing.

I totally agree climate is complex. To my mind, therefore, we should all be scrupulous in our attention to detail and not jump to conclusions. If the data does not support the theory, the theory should be re-visited. Its pointless to keep repeating ‘the fundamental principles work’ when the end result disagrees. Either the fundamental principles are wrong (which I doubt) or they are being interpreted incorrectly (which is probably true). For the cAGW theory to be valid, the temperature should be increasing at an accelerating rate. It is not.

I recall you arguing this same thing over at Lucia’s nearly a year ago. There are quite a few things that can be brought up with respect to the framing of your argument (e.g. aerosols, ocean heat uptake), and it was explained why there is no exact answer for your “how much does CO2 contribute to the current GE” question (due to overlapping absorption bands), but overall the biggest problem is that you don’t seem to understand that the CO2 forcing is logarithmic with respect to concentration. Now, I know you’ve heard these words before, but you don’t seem to understand them…otherwise you wouldn’t be persisting in making an argument based on the assumption of a linear relationship between CO2 concentration and efficacy. If the relationship was expected to be linear, yes, there would be something seriously wrong. But it’s not. The logarithmic relationship means that increasing concentration at lower levels produces a much greater forcing than increasing concentrations at higher levels, which is why the forcing is expressed in terms of doubling rather than absolute increase in ppm. So, for example, you might expect approximately the same forcing change in going from 140 to 280 ppm as you would from 280 to 560 ppm, despite the latter being a larger increase in concentration.

Do you think I am asking this question just to be annoying? If there is no exact answer to the question then why did Lacis, Schmidt et al produce a paper which does exactly that?

Lacis et al 2010:[“Ample physical evidence shows that carbon dioxide (CO2) is the single most important climate-relevant greenhouse gas in Earth’s atmosphere. This is because CO2, like ozone, N2O, CH4, and chlorofluorocarbons, does not condense and precipitate from the atmosphere at current climate temperatures, whereas water vapor can and does. Noncondensing greenhouse gases, which account for 25% of the total terrestrial greenhouse effect, thus serve to provide the stable temperature structure that sustains the current levels of atmospheric water vapor and clouds via feedback processes that account for the remaining 75% of the greenhouse effect. Without the radiative forcing supplied by CO2 and the other noncondensing greenhouse gases, the terrestrial greenhouse would collapse, plunging the global climate into an icebound Earth state.”]

Did you complain to Lacis that he couldn’t give an exact answer? Look at the statement (nb 25% is later refined to 20% for CO2). Is it not explicit? Would you, as a layman, not think that it was a scientifically true statement and that it meant what it said? The trouble is, a moments thought shows why it cannot be true, and yet I am the one you are criticizing!

Please see below my reply to SoD to understand why I am happy to continue to ask the question… and, yes, I understand what you are saying about the log effect…

By your argument, therefore, the next doubling from 560 to 1120ppm will produce another 3.7 Wpm2 forcing, right? According to SoD, that will be another 1 deg C sensitivity (without feedbacks), right? Now figure out how long until we get to 1120ppm and what the likely feedback amount is (do you really think the feedbacks will equate to 200% of the original non-feedback sensitivity?) and we may have some idea of just how much ‘acceleration’ there is likely to be in terms of global warming. The comments on Lucia’s tried to use appeals to scientific authority and not once did they – or you – accept the question for what it was.

You can’t have it both ways. The pro-cAGW ‘consensus science’ cannot claim a high impact from a small amount of CO2 and then claim an increasing impact from an increasing amount of CO2 – and then claim the logarithmic get out of jail free clause without someone shouting ‘foul’.

I don’t care how many times I get a sanctimonious comment from so-called scientists when they can’t be bothered to address the fundamental problem with their theory – the data does not support it! EIther re-visit the theory, or tone down the hype.

Your own chart that shows CO2 IR absorption bandwidth is limited to 600 – 800 cm. However you probably accept that CO2 absorption is confined to the 15uM band with some extension to 14 and 16uM at most.

So, if that zone saturates, how can increasing CO2 make any difference to the rest of the IR spectrum? And as that zone saturates the heating effect must decline proportionately, leading to the results as currently seen – temperature is not rising (missing heat) yet CO2 is still increasing.

There are a steady stream of people visiting this blog insisting that they are correct (on the subject of “saturation”) with no knowledge of any of the research on this subject, and no apparent desire to learn what many decades of atmospheric physics has proven.

I hope you don’t join them – please read all the articles linked and absorb before further comment.

If the fundamental ‘physics’ is so clear, how can 0.028% of the atmosphere cause such a significant portion of the 32.1 C ‘GE’ in 1850, yet a 40% increase of said trace gas only produce an (as yet unknown) portion of a relatively tiny warming of 0.9 C?

This is a fundamental anomaly. I have explained why “thermal inertia’ does not adequately address the anomaly. Your links provide much information about radiation, but not about heat. If your explanations truly can explain CO2′s contribution via experiment, then please explain why the observed evidence does not obviously support the theory.

If you don’t understand non-linear equations – which is the bulk of the real world – then it’s easy to write a question like you pose.

Here is the actual equation used to calculate the effect:

Iλ(0) = Iλ(τm)e-τm + ∫ Bλ(T)e-τ dτ

This is the monochromatic version so of course it then needs to be integrated over all wavelengths.

You can see the beautiful result when measurement of the top of atmosphere spectrum is compared with this calculation:

This image is from Atmospheric Radiation: Theoretical Basis by Richard M. Goody (1989). Note the two spectra are displaced vertically for easier comparison.

The solution to the equation of radiative transfer is what determines how it can be that a small amount of CO2 can have a large effect and a subsequent relatively large amount of CO2 can have a much smaller effect.

It’s there in the equation.

Logic doesn’t dictate that this is a fundamental anomaly. Logic which is based on the flawed assumption that the natural world is governed by linear relationships will incorrectly dictate that this is a fundamental anomaly.

Does this make sense to you?

If not – then it’s reasonable to ask why I should go and review a few papers for you and write up the answer.

So, once again, you decline to answer the question. Please read my reply to ‘troyca’ above regarding the Lacis paper. I made it perfectly clear to you that I was referring to that paper with what I consider to be an anomaly. It is a clear and bold statement about how much CO2 contributes to the ‘GE’. All I wanted was your opinion and how you would come to that opinion. Am I doing this to annoy you? No (although it seems like I am) so please let me remind you about your comments ‘about this blog’:

[precis…]

Science is not a religion.
It’s good to ask questions.
Being skeptical is a positive thing.
…keep asking questions and thinking for yourself.
…the spirit of free inquiry has been squashed.
What lines of evidence support this theory?
What evidence would falsify this theory?
This blog will try and stay away from guessing motives…
And:“It’s harder to understand a new point of view. Or to consider that a different point of view might be right. And yet, more constructive for everyone if we take a moment, a day even, and try and really understand that other point of view. Even if it’s still wrong, we are better off for making the effort.”

SoD, I consider those words to be genuine, intelligent and apt. I have tried to see your point of view regarding non-linear effects but the problem is I can’t get your view to ‘gel’ with the data or the consensus science statements made regarding cAGW. I also note you have ignored my comments on, eg, ‘Inertia’ but concentrate on ‘what appears to be my problem with non-linear relationships’.

All I can say is that it ‘appears’ to me that we are having a non-linear relationship! 🙂

I, as a layman, read the Lacis paper and come away with an opinion. You now refuse to give your opinion as to the answer. If there is no possible answer, I, as a layman, instantly distrust the paper by Lacis as trying to be ‘political’ rather than scientific.

You spoke about logic and asked:[“Does this make sense to you?”]

My answer is ‘yes’. Your statement does make sense. But my logic is not based on an assumption. It is based on the statement in a peer-reviewed pro-cAGW paper. Further, if CO2 contributes 6.6 C to the ‘GE’ today, and the relationship is logarithmic (from troyca), then it must be that, in 1850, CO2 contributed a relatively significant percentage the ‘GE’ then! So how much? Can you answer that one?

If not, I am therefore left with the ‘opinion’ that you are caught in an epistemological vortex due to your belief that the radiative forcing theory is unassailable.

I know the approach though. I’ve explained it a few times and despite you answering “yes” at the end of your last comment above you have filled a few pages with what appears to be a very clear “no”.

When you first asked the question I thought I would find out your approach to the solution because it seemed like a better method of explanation. An engagement rather than an answer. You have treated this as me avoiding the question. But getting “the answer” without understanding the method is, in my opinion, not very useful.

I’ve told you that I have to review some papers to provide the answer. So either you aren’t interested in reading what I write – or have read it but prefer to claim that I can’t answer your amazingly difficult question.

I have lots of people asking lots of questions. I have lots of questions of my own. All of which take time.

It seems you already believe that I “am caught in an epistemological vortex due to my belief“. Not much point then me investing what little time I have in reviewing some papers and writing up some conclusions.

No. Please stop affirming your opinion as to my motive. I just asked you a simple question:

“What do you think is the contribution made by CO2 to the ‘Greenhouse Effect’?”

Please note I was asking for your opinion, not necessarily the definitive answer. That is the ‘What do you think…’ bit. I am somewhat surprised that you do not already have an idea without having to ‘review some papers’. Surely you must have some idea?

[“…your amazingly difficult question.”]

Amazingly difficult? Really? THis should be the question that a climate change scientist should ask him or herself! Closely followed by “how can I quantify the effect of increasing CO2”. If they don’t know what the contribution of CO2 is, then how can they even begin to think they can predict an accelerating and potentially catastrophic increase in global warming?

The thing is, all you really needed to say was “I think it is around xx% but I will need to check some papers to look at it properly…” if you need more time. You run a climate science blog which contains a staggering amount of information. I am somewhat nonplussed that you do not have an idea to hand but of course if you wish to take time to read up on the subject then I can wait patiently.

However, in the meantime, please don’t try to take up your valuable time trying to establish my ‘conceptual errors’, or worrying about my inability to understand non-linear relationships. I am happy that the answer to the question may take a while. Unless you can quantify the exact starting point and the exact nature of the non-linear relationship, there isn’t much point in consensus scientists making bold statements about the future.

For those non-mathematicians curious about the fascinating subject of non-linearity.. (and everyone interested in radiative physics should be at least curious)

Suppose we have an expression which includes the term: e-t – (which is a key term in the equation of radiative transfer).

“e” is an important constant, approximately =2.718, and the expression above is read “e to the power of -t“, or e multiplied by itself -t times. Alternatively 1 divided by [e multiplied by itself t times].

Suppose we double the value t, how does e-t change?

Specifically, what is the ratio r = e-2t/e-t ?

You’re waiting for the answer? No one popping up the Windows calculator and trying it?

So the answer is: “it depends”.

It depends on the value of t. And most people with some vague idea of non-linearity think “ok, might vary by a factor of 10 or 20 then?”

Here’s a graph of the ratio. Note that the vertical axis is a log axis so each major dividing line is a factor of 10:

So as t changes between 0-10, the ratio (e-2t/e-t) doesn’t stay the same, and doesn’t change by a bit or quite a lot, but changes between 1 and 1/20,000 (45 ppm).

Very unsurprising for mathematicians, physicists, chemists and engineers.

Usually very surprising for those without these backgrounds.

So if you want to find out how “the result” changes when “the input conditions” change you have to actually do the calculation. (And in many cases the calculation requires a “numerical” method on a computer, it can’t be done on a pocket calculator).

Intuition, past relationships, and random mental pictures of “non-linear” are no guide at all.

The example above is very simple relationship, provided so readers can try it out on a calculator and confirm the result.

Radiative transfer in the atmosphere requires integrating (“summing”) something like this across millions of absorption lines all of varying strength (ranging by factors of more than a million). Then integrating up through the atmosphere where the line width changes significantly with pressure.

Want to guess the likely range of answers as the concentration changes?

“The question is simple enough. I don’t have a theory and I certainly would not presume to “calculate the effect”! I tend to approach this problem from logic, not science. But I believe that science should at least make sense. I merely question the percentages given by Trenberth and Lacis, so I asked what you think the contribution is. I will, however, expand on my problem with their figures…

Lets take Lacis’ 20% of ‘GE’ is due to CO2:
20% of 33 C is 6.6 C.

In 1850 (the start of IPCC’s ‘accurate data’) the CO2 concentration in the atmosphere was 0.028%. The global temperature was appx 0.9 C lower than today (due to the ‘enhanced GE’ today), source HadCRUt.

Today we have had an appx 40% increase in CO2 with a contemporaneous (but not necessarily caused by) rise of 0.9 C. Today’s ‘GE’ being 33 C.

Therefore, the ‘GE’ in 1850 was 32.1 C. 20% of 32.1 = 6.42 C.

Therefore, Lacis is postulating that a trace gas which caused 6.42 C of the ‘GE’ in 1850, having been increased by a significant 40%, is now contributing 6.6 C to the ‘GE’. This is a rise of 0.18 C. This seems an anomaly. If CO2 makes a significant contribution (20%) to the ‘GE’, why has here not been a significantly greater warming than has been observed?”

There are number of possible reasons:

1. Not the least of which is the non-linear T^4 relationship between temperature and emitted power from S-B (i.e. each additional degree C requires proportionally more and more incident power to effect and sustain).

2. The net feedback to the increased CO2 ‘forcing’ is strongly negative (or at least not positive).

3. CO2 ‘forcing’ has been overestimated and/or has incorrectly assumed all of what’s additionally absorbed by the atmosphere is equal to post albedo solar power all coming down in at the TOA.

4. Changes in the atmosphere system in response to the additional CO2 ‘forcing, dynamic or averaged, are offsetting the effect of the increased CO2 (i.e. making the net effect a wash or zero).

“In fact, I believe that observed data actually tends to support a slightly lower percentage but the exact amount cannot be quantified until someone figures out how much of the observed warming since 1850 (date chosen as being the start of IPCC accurate data, although the IPCC states anthropogenic warming started in 1750) is specifically due to CO2.”

There is currently no way to know how much of the warming (if any) is specifically due to the increased CO2. This is primarily because there are probably more natural forcings we don’t know about than natural forcings we do know about (and could hypothetically estimate).

Having read a few papers on this specific subject, I am unsure how the authors can claim the veracity of their conclusions with such apparent confidence.

Thank you for your points. They make sense to me.

The feedback issue is one I am also nonplussed at in the sense of ‘consensus’ (or IPCC) proclamation. THere appears to be no evidence to support the postulation that feedbacks are likely to cause such a massive increase in climate sensitivity. In fact, considering the evidence that we have had a relatively small increase in gt for a relatively large increase in ‘forcing agents” (assuming – which I don’t – that the effect is significant in the first case), the no feedback CS is currently guessed at around 1 deg C whereas the with-feedback CS is guessed at around 3 deg C.

As the relationship is ‘non-linear’, the observed warming rate is likely to reduce, not accelerate. There is NO evidence for ‘Thermal inertia lag’ and the warming has not increased since 1998.

[“There is currently no way to know how much of the warming (if any) is specifically due to the increased CO2.”]

Absolutely correct. When this sensible point is considered, this would tend to suggest a CS of around 1 deg C with all feedbacks and forcings even if a 50% contribution from CO2 is assumed. Even that is a guess.

The point is no-one knows for sure.

I would like to see some balance and humility brought into the debate, instead of assumption and dogma. I repeat, if the data does not support the theory, then the theory should be revisited. Surely that is in the best interests of Science?

Did you complain to Lacis that he couldn’t give an exact answer? Look at the statement (nb 25% is later refined to 20% for CO2). Is it not explicit? Would you, as a layman, not think that it was a scientifically true statement and that it meant what it said?

From the Lacis et al (2010) paper, they note:

“Because of overlapping absorption, the fractional attribution of the greenhouse effect is to some extent qualitative (as shown by the dashed and dotted extremum lines in Fig. 1), even though the spectral integral is a full and accurate determination of the atmospheric greenhouse strength for the specified global temperature structure.”

Which is the point I was making to there being no exact answer. However, I don’t object to you asking the question (nor do I particularly love the Lacis study), but rather to the argument you made after receiving the approximate answer of 20%.

The trouble is, a moments thought shows why it cannot be true, and yet I am the one you are criticizing!

I am critizing your argument because the “moments thought” seems to assume a linear forcing increase with respect to concentration, which is incorrect.

By your argument, therefore, the next doubling from 560 to 1120ppm will produce another 3.7 Wpm2 forcing, right?

Approximately, yes.

You can’t have it both ways. The pro-cAGW ‘consensus science’ cannot claim a high impact from a small amount of CO2 and then claim an increasing impact from an increasing amount of CO2 – and then claim the logarithmic get out of jail free clause without someone shouting ‘foul’.

I’m not sure if you’re equating me with the “pro-cAGW ‘consensus science'”, but I’ll note that I’ve been focusing quite a bit on the uncertainty in trying to determine climate sensitivity (and the likelihood of an overestimate using this particular method), as you’ll can see at this page: http://troyca.wordpress.com/radiation-budget-and-climate-sensitivity/

Nonetheless, I believe the general argument for why we’ll see an increase in the rate of warming over the next several decades is because a) the ocean heat uptake has damped the surface temperature response so far, and b) the shorter residence time of anthropogenic aerosols means that they will not continue to offset the same percentage of the positive CO2 forcing with increased emissions. While I may be skeptical of the “consensus” magnitude of (a) and (b), it’s worth pointing out the “consensus science” is NOT claiming an increased CO2 efficacy at higher concentrations.

When this sensible point is considered, this would tend to suggest a CS of around 1 deg C with all feedbacks and forcings even if a 50% contribution from CO2 is assumed. Even that is a guess.

The point is no-one knows for sure.

I would like to see some balance and humility brought into the debate, instead of assumption and dogma. I repeat, if the data does not support the theory, then the theory should be revisited. Surely that is in the best interests of Science?

I’m not sure exactly how you came up with 1 degree C, but I agree it is quite uncertain, and the warming over the last century does little to constrain sensitivity (see, for example, this post by Paul_K). This is why we examine other methods to determine sensitivity as well, such as in SoD’s latest post, which also bring in their own question marks. In fact, you may find I generally agree with many of your conclusions regarding the uncertainty (and possible overestimate) of climate sensitivity in the current literature.

However, what is in the “best interests of science” is in putting the best arguments forth for examination. The Spencer and Braswell (2008) argument may have merit, and the point raised by Paul_K is an interesting one as well. However, your argument that we don’t know anything about the effect of CO2 because assuming a linear response leads to absurd conclusions is a weak one, since the “theory” does not suggest a linear response. Those who want the best for the science would like to see the more substantive critiques investigated, rather than allowing the “consensus” to simply lump them in with the weak arguments arising from a lack of familiarility with the basic theory.

[“Because of overlapping absorption, the fractional attribution of the greenhouse effect is to some extent qualitative (as shown by the dashed and dotted extremum lines in Fig. 1)…”]

I know SoD does not like politics, and neither do I, but this makes the point that the part of the paper that gets most publicised is not the ‘extent is somewhat qualitative’ part, but ‘CO2 [by itself] contributes 20% to the terrestrial GE’. It is at this point that ‘Science’ really has to step in to preserve its own integrity and start challenging these claims, not bending over and allowing their good name to be tarnished.

My ‘moments thought’ comment was not meant to appear to be based on a linear assumption. However, if a linear assumption is used, it gets the message across anyway. If a non-linear assumption is made, this actually reinforces my point. The linear relationship would end up with a higher gt than the non-linear. If a 40% increase in CO2 has led to a 0.9C rise in gt (assuming all the warming was due to CO2, which of course is not the case!), then a linear relationship would produce a 2.25C sensitivity (including feedbacks but not including any ‘lag’ effects). If a non-linear relationship exists, then the next 40% increase in CO2 would lead to a smaller warming (say 0.7C? – difficult to say without the actual relationship being known accurately) and the final 20% increase might effect a warming of, say 0.2C. This would total 1.8C for a doubling of CO2. If we ‘assume’ (this is an example as I do hate assumption) that 50% of the warming (since 1850) is due to CO2, then the climate sensitivity would be around 0.9C with all feedbacks and forcings. Hence my figure to you earlier of 1.0 deg C. I have explained why I do not support the ‘inertia’ theory to SoD above.

I was careful not to label you with ‘pro-cAGW consensus science’ as that would be unfair and I have no idea if it is accurate. But you raise an important issue here. And, again, I may stray into politics but only to make a valid point. It is interesting to note that much is being made of uncertainty (as in your blog) at the moment. I applaud you for that. However, not much was being made of uncertainty when the cAGW ‘scare’ was first publicised. Very few scientists (let alone climate scientists) spoke about uncertainty, or smoothing, or lag, or natural variation etc. Very few tried to stop the train pulling out of the station; very few became the small boy in the Emperor’s crowd. End of politics! 🙂

To me, Science needs to get back to what it should be doing, and that is looking at the theory right from square one. Hence, do not assume Arrhenius was correct. Do not assume that the known ability of any individual molecule of CO2 to absorb and re-radiate radiation (in relevant wavelengths) should be faithfully leaped to the conclusion that a truly minute amount of the same gas can have a significant effect on the GE. All I would ask for from Science is some objectivity.

My argument is not simply based on the linear relationship. I hope I have clarified that. I am sorry I don’t have enough time right now to expand further. I will later, if you wish.

I believe my original question to SoD is a valid one, and one that deserves a balanced and objective answer. The Lacis paper (and Trenberth and Schmidt etc) did not, IMO, achieve that.

Going back to the source is always a good idea. A while ago I was having a chat with a climate scientist about Tyndal’s original work back in the mid 1800s and I pointed out that most of his results were related to CO, not CO2. Tyndal was studying Carbonic Oxide (CO) and Carbonic Acid’s (H2CO3) absorption of IR. Tyndal didn’t appear to study CO2 at all. This is according to his original paper titled “On the Absorption and Radiation of Heat by Gases and Vapours” September 1861.

What Tyndall may or may not have studied is irrelevant to what we know now. The HITRAN database of molecular absorption lines was not compiled by Tyndall, but by, among others, the US Air Force for use in satellite imaging and heat tracking missiles. Most of the lines have also been calculated ab initio using quantum mechanics and the known molecular structure. Tyndall was also not aware of important details like pressure and Doppler broadening of spectral lines, or that they were spectral lines rather than bands because the spectrometers of the time had insufficient resolution.

To me, Science needs to get back to what it should be doing, and that is looking at the theory right from square one. Hence, do not assume Arrhenius was correct.

Nothing in the present understanding is based on assuming that Arrhenius was right. On the contrary it’s well known that he erred on many details. All present understanding is built on the present understanding of fundamental physics which builds heavily on QM and Quantum Electrodynamics developed by Feynman and his coworkers.

The mainstream scientists are not those who search their justification from history, that’s done by a part of skeptics. Whenever the understanding of fundamentals changes scientist go always through all fields which may be influenced by that change.

On what Arrhenius did the basic ideas have survived but everything else has changed. That his quantitative estimates were as close to the present understanding is probably more luck than anything more fundamental.

The present scientific knowledge on climate and the Earth system that determines the climate contains both issues that are well known and requires as basis only thoroughly tested physical knowledge, and issues that can not be deduced unambiguously from such fundamentals. Another certain part of knowledge is formed by observations at the level that the accuracy and reliability of observations supports.

This site concentrates clearly on the solid part of the science, i.e. on issues that can be deduced from solid physics and from reliable observations. Less certain results do certainly come up every now and then but they are not the main focus. As far as I can see neither SoD nor most regular commenters make excessive claims on the reliability of those conclusions that do not clearly deserve that. There are other sites that push very strong views, this is not one of those.

“The feedback issue is one I am also nonplussed at in the sense of ‘consensus’ (or IPCC) proclamation. THere appears to be no evidence to support the postulation that feedbacks are likely to cause such a massive increase in climate sensitivity. In fact, considering the evidence that we have had a relatively small increase in gt for a relatively large increase in ‘forcing agents” (assuming – which I don’t – that the effect is significant in the first case), the no feedback CS is currently guessed at around 1 deg C whereas the with-feedback CS is guessed at around 3 deg C.”

I think the purported evidence in support of net positive feedback is extremely weak to say the least. By my own indpth assessment of the evidence, the notion of net positive feedback of 300% acting on energy imbalances in the climate system is so spectacularly flawed it’s ridiculous.

I also think that designating the of often referenced 1.1 C as the ‘zero-feedback’ starting point is not valid, but SoD will not let me discuss this here anymore.

The observed data (I use HadCRUt since 1850 as a rule) is exactly what is says on the tin! It includes ALL feedbacks and forcings. So, lets have a look (I’ve also spoken about this to SoD and troyca above):

An observed warming of 0.9 C in 160 years from a contemporaneous, but not causal, 40% increase in CO2 alone. (By the way, there have been similar of not greater increases in the other non-condensing ghgs…) Even if one assumes (ridiculously) that all the warming was due to CO2, then the sensitivity would be around 2.25C inclusive. There is NO evidence for any ‘lag’ effects, and any lag effects would have already been partially included anyway. So lets revisit how much warming is due to CO2. Nobody knows! However, there have been warmings of similar size to the late 20th century warming before 1950, so it is fair to hypothesize that natural variations play a significant role. So lets say 50% of the warming is due to n-ghgs.

Therefore, a linear-relationshipped answer would be around 1.175C inclusive. However, a non-linear relationship would result in lower figure (by how much? – It depends!). So I think you are correct in doubting the 1.1C figure because that is ‘zero feedback’ and the observed data suggests it is either not valid or highly doubtful.

By using percent increases, you are already using a non-linear response. If we have an initial value of 1 and increase it by 40%, we get 1.4. If we increase again by 40%, the result is 1.96, not 1.8. If you are referring to increments of doubling, then increasing from 1.4 to 1.8 is only a 26% increase and will produce a correspondingly lower increase in forcing than the increase from 1 to 1.4. Also, heat diffusion into the deep ocean does not follow a single time constant, i.e. lag time. At longer times, the effective lag time increases. The turnover time for the entire world ocean is on the order of 2,000 years. We’ve only seen a tiny fraction of that sort of lag time.

..To me, Science needs to get back to what it should be doing, and that is looking at the theory right from square one. Hence, do not assume Arrhenius was correct. Do not assume that the known ability of any individual molecule of CO2 to absorb and re-radiate radiation (in relevant wavelengths) should be faithfully leaped to the conclusion that a truly minute amount of the same gas can have a significant effect on the GE. All I would ask for from Science is some objectivity..

All I would ask for from commenters is to read the articles I point them to and think about them. How is it possible that theory matches the measured spectra at the actual top of atmosphere and surface from downward radiation?

By the way, people who write “do not assume Arrhenius was correct..” just demonstrate their own lack of interest in the scientific subject of radiative transfer. Repeating stuff you read on random blogs without checking it out for yourself just demonstrates a lack of scientific interest.

Check out a textbook on radiative transfer. Does it recite the received wisdom of Arrhenius? No, instead you find references to the theories of Kirchhoff, Maxwell, Stokes, Lambert, Planck, Einstein and Boltzmann – because they are well-tested theories that have stood the test of time. They accurately describe the various physical relationships required to derive the theory of radiative transfer in the atmosphere.

This theory of radiative transfer has also been extremely well tested and is currently used in many practical endeavors, including the measurements of sea surface temperature around the world. The measurements match the results using other methods of measuring sea surface temperature. The theory is also used for measurements of water vapor in the atmosphere & atmospheric temperature. The list goes on. But why bore you with evidence that doesn’t match your needs?

If you read a heavyweight book like Atmospheric Radiation: Theoretical Basis by Goody & Yung (2nd edition 1989) you will find that the references for the basic theory are earlier works like Chandrasekhar 1950. That doesn’t mean that Goody & Yung copied Chandrasekhar, just that they followed a similar approach in their derivation of the theory from first principles.

You can see many pages from the Chandrasekhar 1960 reprint at Google books and even buy yourself a print copy for only $33. A small sum for the knowledge that will save you from writing ridiculous statements in the future.

Personally I am left stupefied by the idea believed by so many internet commenters. That a major theory in physics would just be believed and accepted without being checked from someone writing over 100 years earlier.

I don’t know whether to laugh or cry. The irony is incredible though and that makes me smile.

The irony that the theory that atmospheric physics has accepted a theory without subjecting it to scrutiny is accepted without subjecting it to scrutiny.

I asked you a question several posts ago! You have asked for more time to ‘review some papers’ before answering my ‘amazingly difficult question’.

Since writing those words about reviewing some papers, you have had time to write 5 posts to me alone amassing some 1100 words, most of which have been complaining to me about my ‘conceptual problems’.

I suggest that you could have saved yourself a lot of bother by just answering the question.

If you can’t answer, just say so. It is, however, a basic question which (as I said before) ALL climate scientists should have asked themselves:

What do you think is the contribution made by CO2 to the ‘Greenhouse Effect’?

Now to your ‘experiment=measured’ link.

What part of that link addresses the problem of global warming? I have already said I was happy with the idea of CO2 having radiative properties. The question is how are those properties demonstrated in the ‘Greenhouse Effect’? Read the paragraph you quoted from me in your last post again.

The conclusion that CO2 has a significant effect IS a leap of faith!

Where is the evidence to support the conclusion? A warming of 0.9 deg C in 160 years with no acceleration in the overall trend? A total lack of further warming for over 13 years?

I keep asking you to revisit the theory and all you can do is regurgitate links which do not address the question I asked you. Your link IN NO WAY addresses the likelihood of significant warming.

If you think it has, then where is the warming?

Would you like me to remind you once again of your ‘about blog’ comments?
Oh, ok…

Science is not a religion.
It’s good to ask questions.
Being skeptical is a positive thing.
…keep asking questions and thinking for yourself.
…the spirit of free inquiry has been squashed.
What lines of evidence support this theory?
What evidence would falsify this theory?
This blog will try and stay away from guessing motives…
And:
“It’s harder to understand a new point of view. Or to consider that a different point of view might be right. And yet, more constructive for everyone if we take a moment, a day even, and try and really understand that other point of view. Even if it’s still wrong, we are better off for making the effort.”

Good words!

Please stop trying to belittle my comments when you won’t have the decency to answer my simple question.

You can make all sorts of arguments about why CO2 might not have an effect on the average temperature. But what if you’re wrong? In risk management, you almost never have definitive proof of anything. For example, we have no proof that a large rock will fall out of the sky in the next hundred years and cause a major disaster. So by your logic, we should ignore the possibility that one might fall and devote no resources to finding large rocks that cross the Earth’s orbit or on possible methods of diverting said rock if we find it.

Yes, doubling CO2 might not actually increase average temperature enough to cause significant damage. And possible damage from an increase in temperature may well have been overestimated and costs of mitigation underestimated drastically. But sticking your head in the sand and denying the possibility that something may need to be done isn’t productive. You have to estimate the probability that something bad may happen and also estimate the possible damage from that bad thing. Then you can make a sensible decision about what should be done. So asking for an exact accounting of how much CO2 contributes to global warming currently is pointless. As long as it isn’t infinitesimal, and it isn’t, then the exact amount isn’t important. And as long as the probability of substantial damage isn’t infinitesimal, we do need to consider doing something. And it isn’t.

We should be doing something, but we should be doing things that will be of benefit even if the climate sensitivity is at or below the low end of the IPCC estimate, i.e. no regrets actions. There are lots of them. In other words, skeptics should be concentrating their arguments on the reports from IPCC Working Groups 2 on effects caused by warming and 3 on mitigation reports, not 1 on the fundamental science.

The appeal to the Precautionary Principle is one of the least endearing and most pathetic of all the pro-cAGW commenters’ arguments.

The problem with the PP is that, for it to be effective, a clear and present danger HAS to exist. By your argument, every government in the world should immediately start building massive underground shelters because there is a statistical possibility that a large asteroid could hit the Earth and, if we’re lucky, make the planet uninhabitable. If unlucky, no shelter would be enough.

Against that, the mitigation policies have a rather more immediate effect. Even if all governments agreed and were prepared to think as one.

I realise you are trying to deflect the discussion away from my original question to SoD. Please don’t bother.

I also realise that it is hard for you when someone challenges your groupthink dogma. I’m not sorry about that – the pro-cAGW group deserves it.

If this issue was not around, would anyone look at the temperature record and conclude there is anything unusual or peculiar going on? In particular, something that would require and ‘external’ or non-natural cause?

I think the answer is definitely no, which says an awful lot by itself.

That being said, I don’t think the total CO2 contribution to the GHE is as crucial to the fundamental issue as you think. I have observed that there seems to be no significant disagreement on the +3.7 W/m^2 calculated for 2xCO2 among credible scientists. Furthermore, I know of two scientists – both staunch skeptics, who have actually done the calculation from scratch and are getting about the same quantity.

The question is how much, if any, will this perturbation affect the global average surface temperature and climate. By my own assessment of the evidence, I think the net effect is almost certain to be – if not infinitesimal, benignly small (0.5C or less) Probably too small to even be discerned from the noise of natural variability. I also think any CO2 induced warming is far more likely to be beneficial than harmful. There are also huge benefits to farming, food production and the entire biosphere that come with elevated CO2 levels.

To me the case for net positive feedback – let alone net positive feedback of 300% or more, is so spectacularly flawed it’s ridiculous. And without positive feedback, this whole thing is a complete non-issue.

[“If this issue was not around, would anyone look at the temperature record and conclude there is anything unusual or peculiar going on?”]

Probably not. I think the political ‘ambulance chasers’ have jumped onto the bandwagon in order to make capital out of the idea. That is their job, and they’re a lot better at their job than climate scientists.

[“That being said, I don’t think the total CO2 contribution to the GHE is as crucial to the fundamental issue as you think.”]

Unfortunately, the pro-cAGW camp have made it the issue. The 3.7 W/m^2 issue may well be a red herring. Radiation is not heat. 3.7 is not a significant number anyway in the overall scheme of things.

I completely agree that global warming is likely to be more beneficial than harmful.

I also agree that the feedback issue is the Holy Grail of pro-cAGW posters. Unfortunately for them they don’t have the evidence to back it up.

Logically, if CO2 makes a significant contribution, and their theory is correct, we should have seen a significant and accelerating warming by now, with unmistakeable proof that CO2 is to blame. The fact that we have seen no such evidence is a travesty. Now where have we heard that before?

I know radiation is not heat, but the point is the 3.7 W/m^2 is the reduction in the direct surface to space transmittance, which itself is an all radiative flux from the surface to space.

You question is an interesting and good one, but I agree with SoD that it is enormously difficult to answer. It perhaps more than anything else demonstrates how little is known about the quantity CO2 contributes to the GHE as a whole.

BTW, the answer I would give to your question is about 10% of the total GHE is from CO2.

From this, if about about 300 W/m^2 is absorbed by the atmosphere from the surface LW flux, this would be reduced by about 30 W/m^2 in the absence of CO2. If we assume that about half of what’s absorbed by the atmosphere escapes to space as part of the flux leaving at the TOA, that amounts to a reduction in the net surface flux of about 15 W/m^2. Or about 3 degrees C cooler in the absence of CO2.

The problem of course then is how would this -3C or so affect the components of water vapor and clouds, which could further reduce the temperature? Do you see why this is such a difficult question to answer?

You’re wildly underestimating the effect on temperature of removing all CO2 from the atmosphere. For clear sky conditions, removing CO2 causes emission at the top of the atmosphere to increase by ~30 W/m². That would require a substantial reduction in surface temperature to restore radiative balance. That in turn would require a reduction in specific humidity of about a factor of two in the Tropics or relative humidity would far exceed 100%. The drop in temperature in the tropics would then be greater than 10 C.

[“You question is an interesting and good one, but I agree with SoD that it is enormously difficult to answer. It perhaps more than anything else demonstrates how little is known about the quantity CO2 contributes to the GHE as a whole.”]

Thanks! I know its difficult. That’s why I asked the question of SoD because he at least gives the impression of hosting a balanced and intelligent scientific blog. The reason I ask the question to anyone is because ‘climate scientists’ such as Lacis Trenberth and Schmidt have seen fit to present the answer in their papers or blogs as if it was fact!

Had there been some sort of objective uncertainty producing a balanced conclusion, there would be no need to ask. Unfortunately for them (and the entire pro-cAGW movement), once they make such a firm statement they then have to explain the illogicality of that statement. ‘Non-linear relationships’ and ‘Inertia’ and ‘natural variations’ do not provide a lasting and logical answer to my question.

It is for this reason that I simply ask that they re-visit the theory with an open mind.

[“The problem of course then is how would this -3C or so affect the components of water vapor and clouds, which could further reduce the temperature? Do you see why this is such a difficult question to answer?”]

Yes I do, and thanks for at least answering the question! I believe your 10% is a much more likely figure, although I suspect 5% may be closer still. At least those figures can be seen to be relatively supported by observed data without invoking other assumptive processes.

I have deep suspicions about the veracity of the radiative approach to the GHE. It all comes back to the observed data not fitting the radiative forcing theory without invoking these feedbacks. The figure of 1 deg C warming for a doubling of CO2 may well be correct (apparently it is undisputed – an amazing remark considering the science doesn’t seem to be settled at all…), but IMO it would end there if the observed data is to be believed.

On a lighter note, I am very glad that you and SoD can agree on something! Maybe he can let you continue with your posts on all subjects as a gesture of balance and free speech… 🙂

I used 1.0 C in the same context you used earlier – as the ‘oft referred to zero feedback CS’. However, I agree that 0.5 is at least equally likely. I think feedbacks are not likely to increase the CS by much if anything at all.

As usual, any argument by pro-cAGW commenters about feedbacks is based on assumption and model projection. The evidence just does not support the idea that feedbacks will add 200% to the initial CS figure to get to the IPCC best guess figure.

..I have lots of people asking lots of questions. I have lots of questions of my own. All of which take time.

It seems you already believe that I “am caught in an epistemological vortex due to my belief“. Not much point then me investing what little time I have in reviewing some papers and writing up some conclusions.

I’m not sure what is the correct place to post “where can I read up on xyz?” questions, so here goes.

The chemistry of equilibrium between CO2 in the atmosphere and the top layer of the ocean seems to be:

– not simple

– somewhat controversial

My question: Is there available, on this site or elsewhere, an introduction that can be read by a non-chemist, yet is not over-simplified and will result in sufficient understanding to permit making useful calculations?

Obviously chemical equilibria are the basis of any calculations. I thought that perhaps there might be something that would start from basics rather than assuming the reader had studied chemical equilibria to degree level.

I give you another way of looking to things, using the correct interpretation of Stefan-Boltzmann.
No back-radiation and no crime against the Second Law.
A correct K&T type diagram, where convection of sensible heat and latent heat play the most important role.
Sensitivity analysis gives delta T=0.08 C for doubling the CO2 concentration.

Basic Science is Accepted – This blog accepts the standard field of physics as proven. Arguments which depend on overturning standard physics, e.g. disproving quantum mechanics, are not interesting until such time as a significant part of the physics world has accepted that there is some merit to them.

The moderator reserves the right to just capriciously delete comments which use as their premise that standard textbook physics is plain wrong.

This is aimed to reduce the continual stream of unscientific rubbish that gets placed here as comments.

Comments violating the Etiquette may just be deleted without notification.

JWR: “Back-radiation” is not a crime against the Second Law (2LoT). The 2LoT does not apply to energy transfer between individual molecules by means of photons or collisions. All attempts to apply the 2LoT at the molecular level leads to complete absurdity. The field of statistical mechanics explains how two-way energy transfer between individual molecules always results heat transfer from hot to cold when large number of molecules are involved.

Some collisions between molecules transfer kinetic energy from slower-moving molecules to faster-moving ones. (For example, when the slower-moving molecule strikers the faster-moving from the side.) If such collisions did not take place, all molecules would be moving at the same speed, rather than adopting a Boltzmann distribution of speeds. Why don’t such collisions violate the 2LoT? Kinetic energy is not the same thing as temperature! Temperature – which is proportional to the MEAN kinetic energy – is only defined for large groups of molecules (that are colliding much faster than energy enters or leaves the group). We don’t apply the 2LoT to the behavior of individual molecules because they don’t have a well-defined temperature; just a constantly changing kinetic energy.

Hopefully, you are beginning to see the absurdity of trying to apply the 2LoT to radiative fluxes between the surface and the atmosphere. Given the Boltzmann distribution, it’s possible for an emitting molecule in the colder atmosphere to temporarily have an unusually large amount of kinetic energy and for an absorbing molecule on the warmer surface much less kinetic energy than the average surface molecule. Is a photon traveling between these two molecules violating the 2LoT? How does the photon know that the molecule that emitted it was a faster-moving molecule in a collection of mostly slower-moving molecules. How does the photon know whether to be absorbed or reflected by any particular molecule on the surface? All attempts to apply the 2LoT to the transfer of individual photons between individual molecules lead to such absurdities.

However, everything is much simpler when you consider heat transfer from a large group of molecules on the warmer surface to the a large group of molecules in the cooler atmosphere by photons. Each group has a definite temperature. One group emits oT^4 (or eoT^4 for emissivity leass than 1) , the other emits ot^4 (or eot^4). Heat transfer is the net flux, oT^4 – ot^4, and always goes from hot to cold.

At the molecular level, energy transfer between two molecules by both collisions and photons involves two-way transfer of energy between fast-moving and slower-moving molecules. We have no way of directly observing the two-way transfer of energy by collisions over a fraction of a micron, so we forget it exists. However, we can point an infrared detector at the ground or the sky and observe the two-way transfer of energy by photons over meters or kilometers.

Thank you Frank for your answer.
SoD has already replied.
But Frank, I am an engineer and I compared the one slab model in two implementations: 1) one way proragation of heat and 2) two way propagation of heat. You can see that in the second page of the paper.
I found indeed the same temperature distribution.
But in the two-way proprogation of heat I find that with a heat input of q in the system, the slab absorbs (and emit it again inmedeiately) 2q, twice the amount of heat which is absorbed by the slab in the one-way propagation of heat formulation, a simple one q.
As an engineer I say that the one-way formulation is correct.
In a stack of 50 slabs the slab closest to the ground absorbs 100 q, while in the one-way formulation all 50 slabs absorb a simple one q.

So let us start a discussion which formulation looks the most natural.
They can’t be correct both.

You really should read some Physics Textbooks.
Your “Amazing things we find in textbooks” post was based on authors who thought for the purposes of simplification they could equate infra red radiation as heat and no harm done.

No physics textbook would make the same mistake.

Even the authors themselves if asked would agree with me (and Clausius) if asked whether heat can flow spontaneously from a colder to a hotter object would answer …..no!

JWR and SOD: IMO, the confusion among many skeptics arises because they don’t understand that the 2LoT place any restriction on energy transfer between individual molecules by photons or collisions. The 2LoT demands that heat flow from hot to cold, but individual molecules don’t have a temperature (only kinetic energy). You can’t apply the 2LoT to any situation simpler that two groups of molecules big enough to have a stable mean kinetic energy. The NET energy flux between two such groups by radiation will always flow from hot to cold.

Revolutionary new theories in science are needed when there are observations that are inconsistent with theory. I’d like to believe that some “honest” skeptics would stop hanging out with the Claus and the “Sky-Dragons” if they understood why back radiation doesn’t violate the 2LoT. Unlike most commenters (who seem to be engineers or work with bulk materials), my training is in chemistry. I instinctively try to explain every phenomenon in terms of what molecules do. A simple example of the power of the molecular approach is the derivation of the ideal gas law from the kinetic theory of gases. There’s nothing “fundamental” about the ideal gas law and the reasons why real gases deviate from this law can be understood by examining the assumptions used in the derivation. With the help of statistical mechanics, the laws of thermodynamics and bulk materials have been derived from the physics of individual molecules (ie quantum mechanics). When one understands just a little – that temperature is a bulk property associated with of a collection of molecules – it’s obvious that the 2LoT applies to the NET radiative flux between two groups of molecules, not the separate fluxes.

JWR: I find that slab models of the atmosphere are internally inconsistent. The typical optically-thick slab model assumes that the top and bottom of the slab have the same temperature, with the top surface radiating to space and the bottom surface radiating to the ground. Where does the top surface get it’s energy from? It can’t continuously emit blackbody radiation to space without some source of energy. The slab is isothermal, so energy can’t be transfered through the slab by conduction or convection. It’s opaque, so energy can’t be transferred by radiation. All of these models are missing an arrow showing the energy flux through the slab, which must be equal to the energy flux from the top of the slab to space. If one adds the flux through the slab, you may get a different result.

I am not claiming that the one slab model can represent the atmosphere.
I use the one slab model as a building brick of a stack of slabs.
So let us consider the one slab model as a cooking plate with electrical input such that the surface flux is q watt/m^2.The slab is at a certain distance such that radiation predominates. In steady state the slab emits the same q to the environment.
The question is now
1) the slab absorbs and reemits immediately a quantity per time q as is found in the one-way heat propagation formulation, or
2) the slab absorbs 2q , of which one q is emitted to the environment and the other q is send back to the cooking plate, as is found by the two-way heat propagation formulation.

And in a stack of 50 slabs, the upper slab emits q to the environment.
In the one-way heat propagation each of the 50 slabs absorbs and emits one single q, while in the two-way heat propagtion formulation the slab closest to the cooking plate absorbs 2*50q=100q, and higher slabs gradually less.

The slabs can have a finite thickness and in that case the conduction has to be taken into account for the temperature distribution. But the incoherency as concerns absorption remains.

As an engineer I say that the slabs in a stack of 50 all absorb a single one q.

I find that slab models of the atmosphere are internally inconsistent. The typical optically-thick slab model assumes that the top and bottom of the slab have the same temperature, with the top surface radiating to space and the bottom surface radiating to the ground.

Actually you can solve the energy balance equations around a single slab atmosphere. I highly recommend Grant Petty’s A First Course in Atmospheric Radiation which details the math involved in section 6.4.3. You can read the first part using the look inside feature at a well known on line vendor. Search on ‘single layer, nonreflecting’. The combination of energy absorbed from incoming short wave radiation and absorbed energy from upward long wave surface radiation determines the emission temperature of the layer. And, of course, the emission temperature of the layer will be lower than the temperature of the surface. Willis Eschenbach’s Steel Greenhouse at WUWT is a limiting case where the slab is opaque at all wavelengths.

While I was on the sundog publishing site to get the link for A First Course… I saw a notice for an upcoming book to be published soon: A First Course In Atmospheric Numerical Modeling. Petty has also published another book: A First Course in Atmospheric Thermodynamics that looks interesting too.

The results you get on the multislab model with two way energy transfer appear strange, because the physical system described by that model is strange. Such a system can actually be constructed in laboratory but it’s not a good model for the atmosphere.

The laboratory construction would be based on a large box with vacuum inside. The bottom would be heated by a heat source and the top kept very cold (near 0 K) by cryostatic equipment. Between the warm and hot surface we have thin sheets of metal of surface quality that’s essentially black at IR wavelengths. In this experiment the absolute temperature of second sheet from the top is 1.19 (fourth root of 2) times that of the topmost (T), next has a temperature 1.32T, eight 2T etc. with 50 sheets the lowest has the temperature 2.66T and the bottom of the box 2.67T.

According to the Stefan-Boltzmann law the bottom is really radiating 51 times as much as one surface of the topmost sheet, but it receiving 50 units from the lower surface of the lowest sheet. Thus the net flux is one unit in each gap between the sheets.

For me it’s, indeed, impossible to fully understand why people are not willing to accept that the intensity of radiation can be much higher in each gap than the net energy transfer is – but then my education is rather extreme (I’m by education a theoretical physicist and I have lectured many different courses of quantum mechanics and some of thermodynamics in the early part of my professional career that later led to energy technologies and economics.)

You confirm that the temperature dsitribution in a stack of 50 slabs is as indicated in my paper, both with one-way and the two-way propagation of heat. You confirm that the two-way defenders subtract the two fluxes in order to get the one-way result of a single one q.
But the problem is that in the two-way formulation the absorption in the slabs is many times bigger than in the one-way formulation. In the one-way formulation all slabs absorb a single one q and emit a single one q, in the two-way formulation the slab close to the ground cooking plate absorbs 100q and emits 100q.
Which formulation is correct?
As an engineer I say that the one-way formulation, where all slabs absorb and emit a single one q is correct.
You might give to the slab a finite thickness and take into account conduction.
In the one-way formulation we see again a flux q going through the slab,
the same q as the slab absorbs from the radiation by the cookingplate, and the same q which the slab emits on the other side to the environment.
The two-way formulation of that model with a slab with a finite thickness will have the same temperature distribution, with only one q passing through the slab by conduction. The additional q which the two-way formulation would need is coming from where?
My conclusion is that the one-way heat propagation is the correct one.

And when you read the paper, and even you can skip the algebra just remember that I use equation (1) of the paper to describe the propagation of heat between the grids of the stack, I end up with a K&T diagram without 333 Watt/m^2 back-radiation, without the 324 Watt/m^2 absorbtion in the atmosphere. The window radiation is 52 and the LW radiation into the atmosphere is 16 Watt/m^2.
At that time I claim that the stack model represents the atmosphere.
The missing 179 Watt/m^2 in the radiation balance are from “mechanisms other then LW radiation”: thermals of sensible heat, evaporation and absorbtion by aerosols and ice crystals of incoming sunlight.
Those mechanisms bring the calories towards the IR-sensative molecules higher up in order to be emitted by those molecules to outer space.

Any surface emits at an intensity given by the Stefan-Boltzmann law (assuming that it’s black at relevant wavelengths which is often a good assumption). Thus the warmest surfaces do, indeed, emit at the high intensity. In case of the 50 sheets both surfaces of lowest sheet emit 50 units while one receives and absorbs 51 and the other 49. On microscopic level each absorption and emission of a photon is a separate event. It’s also possible to put radiation probes in the spaces between the sheets and measure both downward and upward radiation intensities which are the full intensities.

Your one-way model is valid for the net flux but not for the emission, absorption, or the radiation intensity in spaces between the sheets.

The situation is exactly analogous in a oven where some body is heated to a high temperature and some walls of the oven are cooled to make them last longer. Measuring radiation levels in neighborhood of such a cooled wall the probe can be found to receive radiation at a power corresponding the wall temperature from one side and at a higher power from the other side. Thus all this is well known in engineering. SoD listed in one of his threads many engineering textbooks showing copies of pages that discuss radiative energy transfer. Thus I cannot see why any engineer would object on the high radiation levels either.

In this way the discussion is not advancing.
Before you were confirming that for both the one-way and the two-way heat propagation formulations the calculated temperature distributions were the same. I have repeated that time and time again in the paper.

I also have made the remark that indeed the net flux (but net flux is a dangerous word in electromagnetic heat propagation!) are the same for the two-way heat propagation formulation and the one-way formulation.
But it turns out that the fluxes which are absorbed (and emitted immediately, because of steady state) are not equal. In a one slab model there is a factor 2, in a 50 slab model it is factor 100.
So please do not come with ovens where locally probes are introduced and the face looking to the heat source measures a higher temperature than the face looking to a cooler wall.

If I summarize the discussion than there is one question:

In a stack of 50 with input in the cooking plate q is the first slab absorbing 100q (and emitting it immediately) as the two-way of heat propagation formulation suggests or only a single one q like all other plates in the stack, according to the one-way heat propagation formulation?

..But in the two-way proprogation of heat I find that with a heat input of q in the system, the slab absorbs (and emit it again inmedeiately) 2q, twice the amount of heat which is absorbed by the slab in the one-way propagation of heat formulation, a simple one q.

As an engineer I say that the one-way formulation is correct.

In a stack of 50 slabs the slab closest to the ground absorbs 100 q, while in the one-way formulation all 50 slabs absorb a simple one q..

It seems you have invented some idea that no one in the field of heat transfer or climate science proposes.

If the first slab absorbs energy at rate q (W/m^2.s) then (under steady state conditions) it emits at rate q. This means each side emits q/2 and therefore the equilibrium temperature can be calculated – so long as you have 2 boundary conditions specified. E.g., q from the inner surface and energy rate or temperature from the utter surface.

In the one slab model the input into the cooking plate is q and in steady state the output from the slab to the environment is also q.
I know that there are one slab models which are teached in universities where they say q/2 to each side, but that is not correct .INPUT=OUTPUT
I know your work SoD and I apprciate it very much.
I am supprised that you make this error.

Why should anyone read anything that starts by a reference to Claes Johnson.

You seem to have some problems in understanding where the factor of two enters. A sheet emitting from two surfaces emits twice as much as one that emits only from one surface (like the ground). That’s natural and there’s nothing in that that should be confusing. You are, however, not the first one who gets confused by that.

And the lower slab near the cooking plate absorbs 100q?
Am I not the first one who does not understand the factor 100?
Let us try to remain serious, and admit that there is a problem when we compare the two formulations: one-way heat propagation or two-way heat propagation.
Temperatures are the same.
But the two-way formulation gives an absorption twice as high as the one-way formulation for the one slab model, and a factor 100 as high for the first slab in the model of a stack of 50 slabs.
In the paper

I have introduced on purpose these simple examples which can be solved by a back-of-an-envelope analysis. For me the factor 2 from the one slab model was sufficient, I introduced the N-slab model to show that for a 50 slab model the factor was 100. In the K&T type budget with the stack model I indeed finf an absorption by the atmosphere of 23 Watt/m^2 instead of the 324 by K&T.

We all agree on the temperature distribution.
Thety are the same for the one-way heat propagation formulation and for the two-way formulation.
In the one-way formulation the lower slab absorbs one sinle q, like all other slabs in the one-way formulation.
In the two-way formulation, with the same temperature distibution, the lower slab absorbs 100q.
So we have to compare q in the one-way formulation with 100q in the two-way formulationThe model is the same: q going into the groundplate and q towards the environment for the upper plate.
One of the formulations cannot be correct.

The lowest sheet absorbs 51 from below and 49 from above. All contrary claims are wrong for this case.

All other sheets than the top one absorb from both sides and emit the average of the absorbed fluxes to both sides. The bottom of the box emits only 51 up and absorbs only the 50 from above. The extra 1 comes from heating. The highest sheet absorbs only from below as the top of the box is near absolute zero and emits (almost) nothing.

Looking at net fluxes only, they are 1 up at every surface.

Still I cannot understand why you make the simple issue so difficult. Where is the persistent error in your thinking?

You just continue to confirm that in the two-way heat propagation formulation the lower slab of a stack of 50 absorbs 100q, where q is the input into the system. Again and again you think you have found that it is indeed 100q, and I started the whole discussion that the lower plate in the two-way heat propagation formulation indeed absorbs 100q.
Our discussion is -and I wonder whether you are aware of that- that in the one-way heat propagation formulation the lower plate absorbs one single q, like all other plates of the stack, in the one-wat heat propagation formulation.

Do you understand the problem?
It are not the individual numbers of the absorption in the one-way and in the two-way formulation we discuss, you agree with the numbers I gave in the paper.
We should find an answer whether the absorption of the single one q of the one-way formulation is correct or the absorption of 100q of the two-way heat propagation formulation.

I have already said that the correct value for that question is 50q from each surface adding to 100q. There’s nothing more to find out. “We” need not find out anything more.

The emission from atoms and electrons near the surface of one sheet is not affected by the presence of other surfaces as long as the temperature is maintained at the same value. Thus it cannot be reduced to zero or one

What makes it so difficult to admit that.

The calculation of net energy fluxes is another issue. Net energy flux is not the same thing as total emission.

Again, you continue to confirm what I wrote in the paper:two-way heat propagation formulation in a one slab model gives twice the heat absorption as compared to the one-way heat propagation formulation, and for a 50 slab model with a two-way heat propagation formulation, 100 times the absorption as compared to the one-way heat propagation formulation.
There is not a problem that I do not admit that the two-way heat propagation formulation would not give the 100-fold heat absorption – I told it you myself in the paper- I only say that in the one-way heat propagation formulation all slabs in the 50 slab model absorb one single q.
For me that is a natural situation.

I therefor prefer the one-way heat propagation formulation.
Applying it to a stack of 50 semi-transparent slabs I find a K&T budget without the 350 Watt/m^2 absorption in the atmosphere.
The LW surface flux into the atmosphere is 16 Watt/m^2 which is absorbed and emitted and half of it is absorbed again.
The model gives as a by-product that the heat flux from the planet is mainly convection of sensible heat(thermals) and latent heat (evaporation).
Radiation is only 10% of the heat evaquation from the surface to the atmosphere the other 90% is taken care of by convection.
By molecular collision – also called conduction or diffusion- the 90% is given to the IR-sensitive molecules – molecules with 3 or more atoms- which are emitting it to outer space.
If you do not accept the one-way heat propagation formulation, you are free to do that. I do not force you to appreciate that the one-way heat propagation formulation gives the results as reported in the paper:

If you have something constructive to say (I accept constructive criticism) please feel free to comment about my question to SoD and his reluctance to answer. If you think you have some real, non-modelled evidence to support the assertion that CO2 can have a significant effect on global temperature then please produce it. If you can answer the question “How much does CO2 contribute to the GHE?”, then please do so.

It has been argued by Claes Johnson that what is called in climate circles
“back-radiation of heat” is not a physical phenomenon. [1, 2, 3]

That’s all I needed to read. I see that the references also include other usual suspects like Nasif Nahle.

One question: If back radiation doesn’t exist, what am I seeing when I point an IR spectrophotometer at the sky and measure a spectrum? Well, not I personally, but it’s being done every day. I have pointed an IR thermometer at the sky and measured a temperature. You could too. They’re cheap.

Don’t expect an extended discussion about this. It’s considered trolling on this site.

CO2 accounts for roughly 10% of the GHE. It accounts for about 1/3rd of the absorption spectrum, but there is considerable overlap from that which would be absorbed by clouds anyway even in the absence of the CO2. On average the Earth is about 2/3rds cloud covered, so that brings CO2’s contribution to roughly 10%.

“I believe your 10% is a much more likely figure, although I suspect 5% may be closer still.”

Yes, it could be closer to 5%, given that much of the CO2 spectrum overlaps with water vapor too. Something like 5-10% is probably a good estimate. I’m afraid you’re not likely to ever get an answer much better or more detailed than this.

Relative to the potential effect of additional CO2, this really doesn’t matter, as the calculation of 3.7 W/m^2 per CO2 doubling includes the reduction from that which would be absorbed by water vapor and clouds anyway (i.e. 2xCO2 alone comes to about 5 W/m^2).

Again, thanks for your information. I am interested in what SoD thinks, as I suspect he will attribute much more than 5-10% to CO2. I am interested to see if he has any evidence to support his estimate. He doesn’t seem to want to answer (in all this time).

It seems as if you are basing your 5-10% estimate on models. Is that true or do you have any real non-modelled data to support it? The radiation based argument doesn’t really explain the estimated contribution in terms of temperature.

You most certainly have not ‘done your best to answer’ my question. You have consistently avoided it.

Your link is meaningless. I repeat my reply to your linked post:
“What part of that link addresses the problem of global warming? I have already said I was happy with the idea of CO2 having radiative properties. The question is how are those properties demonstrated in the ‘Greenhouse Effect’?”

Radiation is not heat.

Come up with something better than “I’m losing interest…”. Don’t try to pretend you are interested in physics if you can’t even try to see the big picture.

I’ll give you a prod:
Lacis thinks it is 20% (plus a further 5% for the other non-condesning ghgs).
Gaving Schmidt thinks it is 26% (dry atmosphere)
Trenberth thinks it is 26% (dry atmosphere)
RW on this blog thinks it is 10%.

What do you think and why?

Oh, by the way, from your ‘About this blog’ section:

Science is not a religion.

It’s good to ask questions.

Being skeptical is a positive thing.

So don’t give me a hard time for agreeing with all of those sentences.

By your queston on CO2’s total contribution to temperature, I assume you mean how much cooler would the Earth’s surface be if there were no CO2 in the atmosphere. As stated before, this is an enormously difficult and pratically impossible question to answer, because trying to determine the net surface temperature manifestation of all the other remaining contributing variables (water vapor, clouds, ice, etc.) is too complicated.

“I assume you mean how much cooler would the Earth’s surface be if there were no CO2 in the atmosphere.”

Yes, that would be a fair take on the question. However, you saying it is ‘enormously difficult and practically impossible to answer’ has not stopped the cAGW politico machine from doing exactly that!

Now SoD wants to paint CO2 and other non-condensing ghgs as the big culprits in the cAGW debate based on his belief in their radiative effect on the climate.

You say it is a difficult question… he doesn’t want to answer… but he also wants us to accept his ‘world view’ without even admitting that to identify the contribution is – according to you – practically impossible. But is it really that difficult? We have plenty of data. Proper, observed data. Non-modelled data.

We have an observed increase in CO2 of about 40% since 1850.
We have an observed increase in global temperature (or as best we can estimate it) of about 0.9C since 1850.

So how can a whopping 40% increase in this amazingly effective non-condensing radiative ghg lead to such a paltry increase? Thermal inertia lag? Feedbacks? No, sorry, there is no proof for either and the planet has had 14 years of no warming to demonstrate some evidence of either. Remember MBH98? No mention of lag there.

Trying to sell ‘radiation physics’ as being the main driver of the GHE might seem fair enough, but it really should have some supporting evidence to be taken seriously.

The likely reason why SoD has given up on you is that you have demonstrated in the past and continue to demonstrate that either you can’t tell the difference between obvious claptrap and actual science or you’re so closed-minded that you will accept anything that fits your prejudices and reject anything that doesn’t.

Your reply to JWR above is an obvious example. It isn’t a great link. It isn’t ‘objective. It’s total garbage. If you can’t see that, you’re hopeless.

I don’t mind you wanting to be SoD’s lapdog, if that floats your boat. I would have thought he could have had a go at answering a simple question without you making pathetic efforts to change the subject.

Either produce some non-cryptic, real evidence or let SoD be the big cheese he purports to be.

It has been a while since I commented here so I would like to wish you all a “Merry Christmas & Happy New Year”.

This site above all others has been an inspiration to me. What little I know about “Climate Science” was learned here. People with totally different views can debate without any name calling and if there is any “Moderating” going on I have yet to notice it.

In particular I would like to thank the host, DeWitt Payne and Leonard Weinstein for sharing their ideas. While I did not always agree, I enjoyed the give and take.

My primary interest is the reform of public K-12 education. Thus far I have helped to create 8 new schools with another 4 in the pipeline. I am working on a series of “Case Studies” intended to help people who may want to start independent schools controlled by the local community rather than state or federal governments. Here is my (pathetic) web site that will hopefully improve over time:http://www.gallopingcamel.info/Education.htm

“Yes, that would be a fair take on the question. However, you saying it is ‘enormously difficult and practically impossible to answer’ has not stopped the cAGW politico machine from doing exactly that!

Now SoD wants to paint CO2 and other non-condensing ghgs as the big culprits in the cAGW debate based on his belief in their radiative effect on the climate.

You say it is a difficult question… he doesn’t want to answer… but he also wants us to accept his ‘world view’ without even admitting that to identify the contribution is – according to you – practically impossible. But is it really that difficult? We have plenty of data. Proper, observed data. Non-modelled data.

Yes, I would say it’s really that difficult and practically impossible to answer. Your question is basically asking if we ‘instantaneously’ removed all the CO2 in the atmosphere, what would the global average surface temperature settle to?

I gave you an answer above about how it would roughly affect the energy balance ‘instantaneously’, but beyond that your not likely to ever get an answer to this question – from SoD or anyone else. Frankly, I fail to see the significance of this question relative to the fundamental scientific question regarding AGW, which the magnitude of the (theoretical) effect.

As far as I know, SoD has not taken an official position on AGW or ‘CAGW’, nor has he taken a position on whether or not the net feedback acting on the climate system globally is positive or negative.

My advice to you would be to focus your efforts on the net feedback question instead.

I appreciate what you are saying but the question IS relevant to the AGW debate and it is perfectly valid.

If we do not know how much CO2 contributed to the GHE before 1850, and how much it contributes to the GHE now, then how on Earth does anybody hope to be able to come up with a realistic figure for climate sensitivity?

Your adjustment of the question (saying it is the same as removing the CO2 instantly) is one way of looking at it, but it is not exactly the same as ‘What is the contribution…”.

If the question is so difficult to answer, why do many of the pro-cAGW commenters seem to have no problem in putting a figure on the contribution? Why does Lacis say 20%, Schmidt and Trenberth say 26%? You have said 10%. All I asked SoD was for his estimate. For some reason, he has taken exception to the question, stating he “needs to review some papers before he can answer”. That was nearly a year ago.

A GHE existed before 1850. That was when the CO2 concentration was about 280ppm. There has been a 40% increase in CO2 since 1850 but the temperature has only gone up by about 0.9C (at the most). No-one can say how much of that 0.9C is due to CO2 but most pro-cAGW commenters (including SoD) seem to think that the radiative effects of CO2 are of high importance re the GHE. So, it is perfectly reasonable for me to ask what the current contribution is.

It should be the most basic question anyone should ask themselves in this debate. IF CO2 makes a significant contribution to the GHE, then this significance should be reflected in the observed temperature, especially as the 280ppm MUST have made a significant contribution to the GHE in 1850 (if the radiative forcing theory is correct). However, if the theory is not correct, then CO2 has had very little significance previously and therefore has very little significance now!

I put it to you that it is DeWitt Payne and Sod that are not listening!

First of all there’s no unique answer to that question because of the overlaps. Depending of the approach the sum of all factors may be significantly more or significantly less than 100%. That’s one reason for the spread of values found in literature.

Second answering that question requires an extensive calculation where a rather detailed description of the present state of the atmosphere is one essential input. Therefore getting an reasonably accurate answer requires so much effort that few people are willing to do that. All we others can only pick one or more of the published analyses and choose our favorite.

Third that percentage is just a number of curiosity value. It’s not an essential input in more relevant calculations but may be produced as a side product of such an analysis. In particular most modelers can probably check relatively easily what the value is in their models description of the atmosphere.

The value of this site (SoD) is in going through science that can be understood step by step and mostly without reference to such tedious calculations as finding out the share of CO2 in the forcing. Stating the personal preferences of that particular number is not relevant or even in line with that approach.

The numbers obtained in recent years by various scientists are close enough when the differences in defining the meaning of the share in forcing are taken into account. The small remaining differences are of little interest. I like most the formulation of Schmidt et al (JGR 2010) that removing all CO2 would cause the net TOA forcing of -27.8 W/m2. That’s more meaningful than any percentage.

Thank you for your post. The reason for my question is not to delve into the realms of curiosity value. I’m looking at the big picture here. The big picture is that the radiative forcing theory necessitates a significant contribution to the GHE by nGHGs. Exactly how much may be of only curiosity value to you, but to the public, figures like 26% represent a very significant amount, especially when it is attributed to a ‘hyped’ gas that is increasing in concentration.

You say: [“The value of this site (SoD) is in going through science that can be understood step by step and mostly without reference to such tedious calculations as finding out the share of CO2 in the forcing. Stating the personal preferences of that particular number is not relevant or even in line with that approach.”]

Unfortunately, the value of this site is undermined by the inability of the host to see beyond his assumption that Arrhenius was correct in his assertion that CO2 was a significant player in the GHE. Everything in the site follows from that assumption. It is therefore a shame that the objectivity required by scientists seems to be missing when it comes to marrying the observed data with the radiative forcing theory.

I repeat – 162 years ago the GHE was only 0.9C less than it is today. Contemporaneously, the CO2 has increased by 40%. IF CO2 had the sort of effect this site suggests, the warming would have been much greater. Lag is not a logical reason. ‘Feedbacks’ is not a logical reason. They are not logical because they are not supported by data.

‘Stating the personal preferences of that particular number…’ may seem irrelevant to you but, in that case, why have they been stated from a political viewpoint, and why were they not refuted or at least challenged by ‘climate scientists’?

Discussion on this site tends to be esoterically limited to radiation.

What I’m trying to do – in spite of being o the receiving end of ‘snark’ from several pro-cAGW commenters – is rationalise the apparent ‘consensus’ view that radiative forcing is a significant GHE player with the observed data which does not validate such a view.

If the debate was about AGRB (radiation balance), I might not ask the question. But its not, its about AGW…

As far as I’m concerned, this is closest thing to absolute proof CAGW can’t happen. It yields an upper bound of about 0.6C for 2xCO2. However, it seems no one in the entire atmospheric science field can understand it, as the methods are different than those traditionally used in climate science.

[“Any number that is not observable and that’s not used as an input or intermediate value in any calculation that aims to produce observable results is of curiosity value only by definition.

If you wish to seriously contest significant scientific results you must look elsewhere and present better substantiated arguments.”]

I’m disappointed. You are evading the point completely. Are you suggesting that if you can’t place the number into an equation for a model that the number is irrelevant? Are you suggesting that the 26% figure issued by K&T, and Schmidt, and 20% from Lacis are significant scientific results when they are based on models?

The ‘observable’ numbers are:

0.9C (= warming since 1850)
40% (= rise in CO2 since 1850)

At which point do you start to trust the observable numbers, and not the model-based numbers?

Finally, how can me asking a question that you, SoD, or any other pro-cAGW commenter is unable to answer, be considered ‘presenting an argument’?

Thank you for the link. I’m sorry you feel that I’m barking up the wrong tree but I still feel my question begs an answer. In fact, the more the pro-cAGW commenters wriggle with an answer, the more determined I am to pursue it. their inability to be objective about the subject is, frankly, mind-boggling.

But are you really looking for an answer? I suspect not, which is fine, as your trying to illustrate a point, but I don’t think you’re likely to convince anyone on either side with it. Good luck in your quest though.

I don’t really expect you to reply to this but, yes, I do expect an answer from at least SoD. I expect a sensible answer! 26% is not sensible. Nor is it reasonable, and yet the pro-cAGW ‘team’ seem to think it is. This shows more about their lack of rational thought than it does about their scientific integrity. Your answer of .6C is far more sensible, so I thank you for that. I will accept that my continuing the search for an answer from those who hold that radiation is the key to the GHE can be seen as ‘making a point’, but the lack of engagement on the illogicality of ‘their’ answers denotes the shallowness of their case.

Nevertheless they still claim some sort of scientific authority. The hubris is staggering. At some point, they will have to accept that the observed data does not support their theoretical world view.

The problem with your link seems to be that it tries to determine the climate sensitivity from radiative balance at surface. That’s not possible because convection and latent heat transfer are so important all the way from surface to the high troposphere.

The better way is to look at the radiative balance at TOA. From that the change in the effective radiative temperature can be obtained by Stefan-Boltzmann law. This is unfortunately more or less the point where the power of simple arguments ends. It’s still possible to say that the imaginary no-feedback climate sensitivity is such that the surface warms a little more than the effective radiative temperature changes. For the real Earth we must include the feedbacks which are beyond the reach of elementary arguments.

The elementary arguments cannot prove or disprove high climate sensitivity.

“The problem with your link seems to be that it tries to determine the climate sensitivity from radiative balance at surface. That’s not possible because convection and latent heat transfer are so important all the way from surface to the high troposphere.”

No, there is no radiative balance at the surface, but because the surface is so close to a black body, it radiates the same amount of power it is supplied as a result of all the physical processes in the system (both radiative and non-radiative).

The key is understanding that the dimensionless gain used in the sensitivity part of that analysis quantifies the same thing and has the exact same physical meaning as how they define feedback in traditional climate science. That is, the dimentionless ratio of power densities at the surface and TOA provides a direct measure of everything that happens in between the surface and TOA – both radiative and non-radiative (known and unknown).

At an average temperature of 287K, the absolute ‘gain’ is about 1.6 (i.e. 385/239 = 1.61). For warming, a response less than the absolute gain indicates negative feedback and a response greater than the global gain indicates positive feedback.

If this is still perhaps not clear, consider that the so-called ‘zero-feedback’ Planck response of about 3.3 W/m^2 per 1C of warming is itself directly derived from the global dimensionless gain ratio of 1.6 (i.e. +1C = +5.3 W/m^2 from S-B; and 5.3 W/m^2/1.6 = 3.3 W/m^2).

No, there is no radiative balance at the surface, but because the surface is so close to a black body, it radiates the same amount of power it is supplied as a result of all the physical processes in the system (both radiative and non-radiative).

The basic logic goes as follows. This is heavily simplified but good enough for the logic.

– Radiative balance is formed at the top of troposphere. There’s a lowest level where convection is not needed for energy balance as radiative processes are in balance and result in a lapse rate equal to the adiabatic one without any convection.

– At all lower altitudes the lapse rate is determined by convection. The actual value is the environmental lapse rate that’s not exactly the same as dry or moist adiabatic lapse rate but closely related to those.

– The amount of convection and latent heat transfer is determined together with the lapse rate.

– The temperature profile near to the surface forms to be in balance with the above factors. Among the factors that affect this balance and are fixed by the requirement of the balance are the surface temperature and radiative fluxes to and from the surface as well as other energy fluxes of the surface.

The radiative balance at the surface is part of the last step in this chain of control. It adjusts automatically to the requirements set by the other factors. Therefore it’s among the most difficult of all to interpret.

I don’t believe that there’s any valid argument to support the particular gain of 385/239. The “gain” is less without feedbacks (roughly 1.2) but with feedbacks there are no simple valid arguments to fix the “gain”.

The net radiative heat transfer from surface is rather small. Trenberth-Fasullo-Kiehl (2009) estimate is 63 W/m2, other estimates vary but are of the same order of magnitude. Stefan-Boltzmann law applies to the gross and not to the net and is of little significance in the consideration of the surface energy balance as the net value depends on the temperature profile of the lowest atmosphere and is through that part of the automatic adjustment.

The surface is considered to be at a state of energy balance when energy gain equals energy loss, right? So at 287K, the energy gained or supplied to the surface is about 385 W/m^2, right? This is also the amount of power the surface radiates into the atmosphere, right?

For example, if the surface temperature is to increase by 1.1C from a baseline of 287K, the net energy flow (i.e. power) supplied to surface has to increase from about 385 W/m^2 to about 391 W/m^2, which in turn increases the amount of power radiated from the surface into the atmosphere by 6 W/m^2 (from 385 W/m^2 to 391 W/m^2). 3.7 W/m^2 x 1.6 = 6 W/m^2. The so-called ‘zero-feedback’ response to 2xCO2 is about 1.1C, correct?

For 3.7 W/m^2 from 2xCO2 to cause an increase in temperature of 3C, the energy supplied to the surface has to increase by about 16 W/m^2, which requires dimentionless gain of 4.3 (i.e. 16/3.7 = 4.3), which is nearly 3x greater than the so-called ‘zero-feedback’ gain of 1.6.

RW has a unique approach to the subject not taught in any textbooks, and counter to all heat transfer textbooks.
He keeps referring me to George White’s analysis. George also has this same unique approach.
I have given up on responding to his repetition of confusion.

– Radiative balance is formed at the top of troposphere. There’s a lowest level where convection is not needed for energy balance as radiative processes are in balance and result in a lapse rate equal to the adiabatic one without any convection.

– At all lower altitudes the lapse rate is determined by convection. The actual value is the environmental lapse rate that’s not exactly the same as dry or moist adiabatic lapse rate but closely related to those.

– The amount of convection and latent heat transfer is determined together with the lapse rate.

– The temperature profile near to the surface forms to be in balance with the above factors. Among the factors that affect this balance and are fixed by the requirement of the balance are the surface temperature and radiative fluxes to and from the surface as well as other energy fluxes of the surface.”

I have no real disagreement with any of this, BTW. I do not see it as being in conflict with the above linked analysis.

Those calculations do not show anything because the net radiative energy transfer from the surface changes much less. How much it increases from 63 W/m2 is not obvious because more CO2 and warmer atmosphere both add to the flux from atmosphere to the surface. The change in this balance is exactly the difficult-to-estimate last step in the chain of control that I mentioned in my previous comment. A detailed analysis of all processes is needed to determine the effect. Even the best atmospheric models cannot do that calculation very well.

No fundamental principle set relevant limits on the “gain” in the radiation from the surface. There are more obvious limits for the net radiative heat transfer but as I explain above that by itself does not determine the gross emission or temperature of the surface.

The concept of “gain” doesn’t appear useful as the controlling mechanisms are totally different, i.e. mainly convection and water cycle and the related atmospheric processes (clouds etc.). Radiative energy transfer and GHE is needed to drive the atmospheric heat engine but is not the controlling process within the troposphere or at the surface.

“RW has a unique approach to the subject not taught in any textbooks, and counter to all heat transfer textbooks.
He keeps referring me to George White’s analysis. George also has this same unique approach.
I have given up on responding to his repetition of confusion”

Yes I know, though I appreciate you at least taking the time to listen. No offense, but I think it’s pretty sad that apparently no one can understand it. The methods are different for sure, but have some really big advantages over those currently being used in climate science. White is approaching it more from systems engineering approach, which is faking everyone out.

A short comment on Miskolczi. I noticed that you referred to his 2010 paper as interesting. I had thought that it would be as fully wrong as his earlier paper, but realized that it was, indeed, a mixture of rather interesting calculations and erroneous conclusions. In particular I got the impression that he was very close to making a reasonable calculation of climate forcing for the simplified atmosphere he was analyzing.

More specifically this Figure 6 from his paper serves as a possible starting point for understanding how the OLR at TOA is formed. Repeating that calculation with more CO2 should give an estimate for forcing that’s in the right ballpark in spite of the simplifications of his atmosphere.

“Do you agree that the surface is emitting about 390 W/m^2 solely due to its temperature and nothing else (assuming an emissivity of 1 or very close to 1)?”

You answered yes to this question, which I asked for a very specific reason.

Now, think about this very carefully. If the surface is emitting 390 W/m^2, then it must have an incoming energy flux of 390 W/m^2 in the steady-state, right? There is 240 W/m^2 coming in from the Sun and 240 W/m^2 leaving at the TOA, right? Where is the additional incoming flux of 150 W/m^2 at the surface coming from to get the total of 390 W/m^2 (240 + 150 = 390)? This has to be coming from somwhere, right?

Your convection/latent heat flux of 100 W/m^2 is a net zero flux at the surface, because 100 W/m^2 is leaving the surface and 100 W/m^2 is returned to surface. In other words, 100 W/m^2 is entering the atmosphere from the surface and 100 W/m^2 entering the surface from the atmosphere.

However, at the TOA, only 240 W/m^2 is entering and leaving, so yes energy in = energy out, but where is the additional incoming 150 W/m^2 flux at the surface coming from?

Just a nonsense set of statements. The first law of thermodynamics is very simple and when we apply it to the surface we find that the fluxes all balance.

When we apply the same first law of thermodynamics to the complete climate system we find the fluxes all balance.

Inventing rules that have no thermodynamic basis and contradict the basic laws of thermodynamics is not a “systems engineering approach”, it is just wrong.

[“…At all lower altitudes the lapse rate is determined by convection. The actual value is the environmental lapse rate that’s not exactly the same as dry or moist adiabatic lapse rate but closely related to those.”]

This is wrong on two counts.

The lapse rate is not determined by convection, it is the other way around. Convection is determined by the (environmental) lapse rate. The adiabatic lapse rate is not related to the environmental lapse rate except insofar as the amount of convection depends upon the difference between the ELR and S/DALR (and RH).

“Any surface emits at an intensity given by the Stefan-Boltzmann law (assuming that it’s black at relevant wavelengths which is often a good assumption”.

The only surface in the climate system is the one at the bottom. Models, of either one-way or two-way radiation fluxes, which incorporate “n surfaces” in the atmosphere where “n” is usually taken as 2 for pedagogic purposes, it seems to me are too unrealistic to be useful and may lead to false teachings.

Wouldn’t it be more realistic to model the atmosphere as “slabs” in which the mass of radiatively-active molecules, the efficiency per unit mass of radiative activity (absorption and emission) and temperature of the radiative activity all diminish with altitude? If so, these three qualities together would be a measure of the energy density of the slab. Now, wouldn’t energy spontaneously flow from a slab of higher energy density to one of lower energy density, that is, one way and upwards?

To have a realistic view of the atmosphere neither sheets nor slabs are appropriate as gas is neither.

I discussed the case of thin sheets because that’s a physically realizable system and it’s therefore possible to discuss it without unrealistic simplifications.

The radiative heat transfer may be discussed also in gas in terms of photons that go in all directions. The mean free path varies depending of the wavelength and the density of the gas. In some cases the mean free path is so short (like a few meters) that it can be handled similarly with conduction using the diffusion equation. In such cases forgetting the intensity of overall radiation is a reasonable choice. Then only the “one-way” conduction-like heat transfer is observed. In other cases the mean free path is so long (hundreds of meters or more) that description as a diffusion process fails due to the finite (non-differential) temperature difference between the point of emission and point of absorption.

Looking at microscopic level the radiative energy transfer occurs always in all direction but so does even conduction. On macroscopic level we don’t see individual photons or molecules but only variables like temperature and pressure. In terms of these macroscopic variables heat flows along temperature gradients from warmer to colder, but that refers only to the net sum of all the microlevel transfers that go in all direction.

That would not model correctly the atmosphere as the radiative processes of the atmosphere are affected by the mean free paths or in other words by the wavelength dependent opacity. To get that right we would need transparency as well for the sheets.

I thought transparency was implied by my use of the term ‘grey’. Absorptivity, reflectivity and transmissivity must sum to 1. If we specify reflectivity ≡ 0, anything that isn’t absorbed is therefore transmitted.

This is a common problem with simplified examples that are not specified very carefully. People fill the missing information differently and then disagree on the outcome – sometimes only because they have a different setup in mind. In one of my above messages I did specify carefully the setup I had in mind and that was built from thin metal sheets in a vacuum box.

The statement to which I was replying is not your original formulation of a vacuum box with multiple metal sheets. It’s this:

To have a realistic view of the atmosphere neither sheets nor slabs are appropriate as gas is neither.

My reply still stands. Sheets or slabs are appropriate to model the atmosphere if they have the correct optical properties. An absorptivity that doesn’t vary with wavelength is not a correct optical property.

JWR: Does it make a difference if you think in terms of heat transfered, q, rather than power, in your multislab models. When you give the bottom slab a heat source, you are actually talking about power and the temperature build up in the bottom slab depends on how fast that energy can escape through all of the slabs. You might consider reading one of SOD’s earlier posts on this subject:

No, in the model I can give as boundary condition the surface flux or the surface temperature. For a prescribed surface temperature I use the technique of Lagrange multipliers, but any other technique will do.
In fact, in most of the examples I do not solve the equations – only in the example of a stack in vacuum I solve the 50×50 matrix, which takes less than 20 seconds on my PC.
I rather use the temperature distribution defined by the environmental lapse rate and calculate the necessary heat input- at the ground level and along the complete air collumn. I found indeed that the LW radiation from the surface is only 16 Watt/m^2 , about 10% and the other 90% is transported to the higher atmosphere by convection.
From there the heat brought by the O2 and N2 molecules is given by molecular collision – also called diffusion or conduction- to the IR-sensative molecules (molecules with 3 or more atoms).
You can read that in more detail in the paper:

JWR: No one here believes that back radiation of heat (from the atmosphere to the surface) exists. We recognize that statements saying or implying that back radiation “warms” the earth or makes it “warmer” can lead to misunderstanding. We simply believe that the 2LoT refers to the net flux of what you call two streams.

You haven’t engaged on any of the points I made about about whether the 2LoT places any restrictions on the behavior of individual molecules:

1) Isn’t the behavior of bulk materials like the atmosphere and the surface of the earth produced by the net behavior of the individual molecules that make up the material? (After answering, read the first paragraph of:http://en.wikipedia.org/wiki/Statistical_mechanics)

2) In your words, the 2LoT makes it a crime for heat to flow from cold to hot. To decide whether a crime has been committed when energy is transferred between two molecules, we need to know which one was hotter and which one was colder. Do individual molecules have a temperature?

3) Do you believe that a slower-moving molecule can strike a faster-moving molecule from the side and transfer some of its kinetic energy to the faster-moving molecule? Do you believe that such collisions create the Maxwell-Boltzmann distribution of molecular speed in a gas? Do collisions that transfer kinetic energy to a molecule that already has more kinetic energy violate the 2LoT?

4) Can a photon be emitted by a faster-moving molecule and absorbed by a slower-moving molecule? (“Faster moving” here means more kinetic energy.) Does it make any difference whether the faster-moving emitting molecule is found in the midst of many other molecules with much less kinetic energy (ie colder) than the emitter or the potential absorber? If so, how does the potential absorber know that the emitting molecule was surrounded by molecules with less average kinetic energy than the absorbing molecule’s neighbors?

Frank
I am not afraid, but I do not have the expertise to go into the subjects you want me to engage in.
This said, I am glad to hear that you too do not believe in back-radiation.
I found a way to circumferent it by writing the Stefan-Boltzmann law as a one-way traffic, from warm to cold, as indicated in my equation (1), and I say it as a philosophy “identify pairs to exchange heat from warm to cold.
There might be other ways, on the molecular level, to arrive at the same result.
I will send your questions to Douglas Cotton who has been involved with the problem on a more physical base than me, I have an engineering approach.

The results of my stack model are such that I believe that I have found a what is called a K&T diagram which is closer to the reality as I have seen up to now.
Heat is mainly leaving the surface by convection, about 100 Watt/m^2. The remaining 68 are leaving as LW radiation, 52 through the window and 16 Watt/m^2 LW radiation is absorbed (as a global and annual average of course) by the atmospheric IR-sensative molecules with 3 or more atoms and are emitted again. Half of them are going to be absorbed for a second time and re-emitted again.

Using the two-way description of radiation is superior in practice when we move to more realistic cases from the simplified case we have discussed. Keeping track of all pairs of surfaces or volumes of gas separately is much more complex than looking at each individually in combination with the radiation intensity that hits it. For that reason your preferred choice is not good in practice.

The more serious problem with your paper and some of your earlier comments is that you are not satisfied with describing the correct physics in another way. That could be considered a matter of taste. But it’s not any more a matter of taste when you start to draw erroneous conclusions or start to claim that the standard approach is against the Second Law. When you proceed to those claims then you are strictly wrong and not only someone who wants to use a different language to discuss the correct physics.

In your conclusion you claim that you have “identified fundamental errors of IPCC authors”. In such claims you are fundamentally wrong.

If you insist on using a different language from the scientific community it’s your choice but then you must know that others don’t use the same language and that your choice of language does not influence to the least the validity of the work of the scientists. (The handful of people who try to prove established physics wrong in related ways may agree with you but with a little more learning you should start to see how terribly they fail every time.)

JWR wrote: “I am not afraid, but I do not have the expertise to go into the subjects you want me to engage in … I will send your questions to Douglas Cotton.” Based on past conversations, I believe you’ll find that Doug Cotton has no answers to these questions either.

If you don’t understand why temperature is a bulk property (proportional to the mean kinetic energy of a group of molecules colliding faster than they transfer energy outside the group, ie in local thermodynamic equilibrium), perhaps you aren’t qualified to write about the 2LoT. Can you really talk intelligently about the 2LoT when you don’t fully understand what hot and cold says about the molecules emitting and absorbing photons?

Your movement appears to be based on ignorance of what accepted physics says about the behavior of molecules and how the macroscopic properties like temperature, entropy and the 2LoT arise from this behavior. Assuming you don’t wish to remain ignorant about this critical subject, you have a choice: a) Learn why the 2LoT applies to the NET transfer of radiation (heat) between two groups of molecules, then accept that the conventional two-stream model is correct and that pyrometers measure IR as they were designed to do. b) Believe that the 2LoT prevents photons from traveling from any molecule in a colder region to any molecule in a hotter region, and devise some scheme that allows a photon to know the local temperature it is coming from and going to (so it can decide whether being absorbed is a crime). Even if you ignore all of the evidence that shows that electromagnetic radiation is quantized, you still have the problem explaining how a wave traveling from one molecule to another can correctly respond to the mean kinetic energy of nearby molecules.

Option A does NOT require you to believe that: 1) Back-radiation transfers heat from the colder atmosphere to the hotter surface. 2) NET radiation is a more important mechanism of cooling the surface of the earth than convection. 3) Warming caused by 2X CO2 will be 2.0-4.5 degC.

You do know that the Stefan-Boltzmann equation is the integral over all wavelengths of the Planck equation don’t you? There is only one temperature in the Planck equation. Your so-called correct version of the S-B equation is actually a reduced form of the equation to calculate net heat transfer between planes assuming an emissivity and view factor of 1 for both planes. It is identical to the difference between the S-B equations for each plane.

The problem for Claes Johnson is that it’s not just the photoelectric effects response to light frequency that he has to explain, but also the random nature of the emission of the electrons at low light intensity as a function of time. His theory has to be able to calculate the molecular absorption spectra for EM radiation, not to mention radioactive decay. It’s conceivable that he could do this, but it’s like the Ptolemaic system of epicycles. Sure it’s possible to transform coordinates to put the Earth in the center of the universe and explain astronomical observations, but the math becomes much more complex.

One of the founding fathers of QED, Richard Feynman, has called it “the jewel of physics” for its extremely accurate predictions of quantities like the anomalous magnetic moment of the electron, and the Lamb shift of the energy levels of hydrogen.[1]

Sure it doesn’t explain why particles have the masses they do, but neither does CJ’s theory. The point is that QED works and it works very well. To replace it, you need something that works better. That hasn’t happened yet. What there is of CJ’s theory is incomplete and appears to be contrary to actual observations. He can handwave all he wants to about pyrgeometers, but that doesn’t explain the observations of Fourier Transform Infra-red Spectrophotometers like the AERI.

If you mix in DG you make only a disservice to yourself and everyone. He has been banned from most climate sites for pushing aggressively his own non-sense paper. If you cannot get rid of people like CJ and DG you have no hope of learning anything.

JWR’s BS detector is either broken or non-existent if he can’t see through DC, CJ and NN. He may have an engineering degree, but I certainly wouldn’t hire him for doing any sort of original work based on that alone.

“The numbers obtained in recent years by various scientists are close enough when the differences in defining the meaning of the share in forcing are taken into account. The small remaining differences are of little interest. I like most the formulation of Schmidt et al (JGR 2010) that removing all CO2 would cause the net TOA forcing of -27.8 W/m2. That’s more meaningful than any percentage.”

That is almost exactly my estimate from above, which was about a -30 W/m^2 at TOA (i.e a total absorption decrease of about 30 W/m^2).

“Those calculations do not show anything because the net radiative energy transfer from the surface changes much less. How much it increases from 63 W/m2 is not obvious because more CO2 and warmer atmosphere both add to the flux from atmosphere to the surface. The change in this balance is exactly the difficult-to-estimate last step in the chain of control that I mentioned in my previous comment. A detailed analysis of all processes is needed to determine the effect. Even the best atmospheric models cannot do that calculation very well.

No fundamental principle set relevant limits on the “gain” in the radiation from the surface. There are more obvious limits for the net radiative heat transfer but as I explain above that by itself does not determine the gross emission or temperature of the surface.

The concept of “gain” doesn’t appear useful as the controlling mechanisms are totally different, i.e. mainly convection and water cycle and the related atmospheric processes (clouds etc.). Radiative energy transfer and GHE is needed to drive the atmospheric heat engine but is not the controlling process within the troposphere or at the surface.”

Relative to the main issue of contention regarding AGW is the magnitude of the effect, right? That is how much will 2xCO2 increase the energy supplied to the surface (thereby increasing the surface temperature), right?

Do you agree that because the surface is so close to a black body, the amount of energy (i.e. power) it radiates into the atmosphere is, for practical purposes, the same as the amount of energy it is supplied?

I assume yes to both of these (if not, please explain). Do you agree that power in W/m^2 is slaved to temperature via the S-B law? That is, if you have a measure of the temperture at the surface, you can deduce the net power supplied to the surface from the S-B law? From which, you can also deduce the power radiated from the surface?

This is all George White is doing, and is what he means when he refers to the ‘surface power’.

That was from a discussion related to something else, which is – I guess, more controversial. Not what I’m referring to here. Notice I have assumed the 3.7 W/m^2 of GHG ‘forcing’ from 2xCO2 is equal to that of post albedo solar forcing.

“When people write nonsense and pass it off as innovative steps forward then there is a lot of potential for sadness on the part of the “innovater”.

Suit yourself. I’m confident what I have written here in this thread is correct. Everyone can and should decide for themselves, of course.

BTW, I’ve given up on the GHG ‘forcing’ halving issue. Unfortunately, I do not have the ability to do the RT simulation/calculation myself, so I really don’t know. Maybe GW’s intepretation of the physical meaning of the 3.7 W/m^2 is not correct, even though Myhre himself seemed to confirm it. I really can’t verify it definitively. All I can say if it is correct, then I’m pretty sure GW is at least basically correct. But again I really don’t know and can’t say. Hopefully that is fair enough from my end.

Relative to the main issue of contention regarding AGW is the magnitude of the effect, right? That is how much will 2xCO2 increase the energy supplied to the surface (thereby increasing the surface temperature) after feedback, right?

Do you agree that because the surface is so close to a black body, the amount of energy (i.e. power) it radiates into the atmosphere is, for practical purposes, the same as the amount of energy it is supplied?

I assume yes to both of these (if not, please explain). Do you agree that power in W/m^2 is slaved to temperature via the S-B law? That is, if you have a measure of the temperture at the surface, you can deduce the net power supplied to the surface from the S-B law? From which, you can also deduce the power radiated from the surface?

This is all the author is doing, and what he means when he refers to the ‘surface power’.

Do you agree that because the surface is so close to a black body, the amount of energy (i.e. power) it radiates into the atmosphere is, for practical purposes, the same as the amount of energy it is supplied?

The average emissivity of the surface in the LW band is very close to one. However, radiant power ≠ absorbed power. That’s because there is net flux by convection, latent and sensible. In fact, significantly more convective net flux than radiative, ~100 W/m² net convective flux vs ~70 W/m² radiative flux. An increase in surface temperature would result in a net decrease in radiant flux and an increase in net convective flux to a first approximation. A purely radiative energy flux lapse rate is much higher than the adiabatic rate near the surface. Convection must then ensue, cooling the surface below the purely radiative steady state temperature. Global net energy flux by convection from the surface to the atmosphere is required for a system like the Earth’s. And to forestall your usual response, no, none of that ~100 W/m² is transferred back to the surface anywhere by convection. It goes into the atmosphere and is radiated away to space.

Yes. The energy balance at the surface is the sum of all of the effects and their complex interdependencies. This is because on average the surface receives more direct radiative power from the atmosphere and Sun than it emits, but much of this direct radiative power is replenishing non-radiative power leaving the surface (primarily as latent heat) but not returned, making it net zero energy flux entering the surface. My point is the sum of all the fluxes incident on and leaving the surface must be about 385 W/m^2 for 287K, which then is also the amount of power directly radiated from the surface.

That simply for 287K the amount of energy (i.e. power) ultimately supplied to the surface is about 385 W/m^2. Because the surface’s emissivity is so close to 1, it means that a watt of incident radiative power from the atmosphere is about equal to watt of incident non-radiative power from the atmosphere. Thus, the net energy supplied to the surface, regardless of how it is ultimatley manifested at the surface, is the same as the energy directly radiated from the surface.

Specifically, a ghg forcing of 3.6 W/m² at the TOA is supposed to be equivalent to a reduction in albedo corrected solar radiation of 3.6 W/m², not 1.8 W/m². That’s the definition of forcing. Using the seasonal cycle to diagnose climate sensitivity only gets you the sensitivity for time scales less than six months. That’s going to be fairly close to the Planck feedback sensitivity.

I have not said much about the GW text. It’s just a short rather incoherent paper that doesn’t explain sufficiently its ideas to make it clear what the author has done or thinks. There are also serious errors in the test like this one:

According to HITRAN based simulations, the atmosphere captures 3.6 W/m² of additional power when the CO2 is increased from 280ppm to 560ppm. Of this, the atmosphere radiates half of this up and half down.

Atmosphere does not radiate half up and half down. Any small volume within atmosphere does that but not the whole atmosphere because the bottom is much warmer than the top and radiates much more for that reason.

The text sentences on what happens to the radiation from surface lacks all justification. They are just declarations of the author without any obvious basis. Not surprisingly the following conclusion on the surface temperature change is also unjustifiable and wrong.

I think I have had enough of this. It’s unlikely that I’ll respond to any further comments on this subject.

“Atmosphere does not radiate half up and half down. Any small volume within atmosphere does that but not the whole atmosphere because the bottom is much warmer than the top and radiates much more for that reason.”

Yes of course. That’s NOT what GW is saying in the quoted section (i.e. that the atmosphere is isothermal), but I don’t want to get into a detailed discussion about that.

“The text sentences on what happens to the radiation from surface lacks all justification. They are just declarations of the author without any obvious basis. Not surprisingly the following conclusion on the surface temperature change is also unjustifiable and wrong.

I think I have had enough of this. It’s unlikely that I’ll respond to any further comments on this subject.”

Suit yourself. With a little effort though, I think it’s pretty easy to understand what he’s doing and why it is valid.

With a little effort though, I think it’s pretty easy to understand what he’s doing and why it is valid.

Yes to the first part and no to the second. His logic isn’t valid. The forcing of 3.7 W/m² is the drop in radiation upward at the TOA after the stratosphere is allowed to equilibrate from doubling CO2. It says nothing about where that energy goes. GW’s statement that half goes up and half goes down is wrong. Initially, none of it goes up by definition. Everything that follows from that statement is therefore also wrong.

What’s important is how much the surface temperature and the temperature of the rest of the atmosphere has to increase to restore radiative balance at the TOA again. That’s about 1.2 K for the Planck feedback alone. Any increase in specific humidity will increase that value. The sign of cloud cover feedback is uncertain. Any reduction in the average land and sea ice cover will be a positive feedback.

Specifically, a ghg forcing of 3.6 W/m² at the TOA is supposed to be equivalent to a reduction in albedo corrected solar radiation of 3.6 W/m², not 1.8 W/m². That’s the definition of forcing. Using the seasonal cycle to diagnose climate sensitivity only gets you the sensitivity for time scales less than six months. That’s going to be fairly close to the Planck feedback sensitivity.

“Yes to the first part and no to the second. His logic isn’t valid. The forcing of 3.7 W/m² is the drop in radiation upward at the TOA after the stratosphere is allowed to equilibrate from doubling CO2. It says nothing about where that energy goes.”

Funny that you should say this, as the IPCC’s definition of RF is all that of downward radiated power (i.e. “net (down) minus up irradiance” and not ‘minus up irradiance’).

“GW’s statement that half goes up and half goes down is wrong. Initially, none of it goes up by definition. Everything that follows from that statement is therefore also wrong.”

All he’s saying, independent of the reasons why he’s saying it (for which I don’t want to get into), is that upon its initial re-radiation by the atmosphere, half of the newly absorbed energy will be radiated back up in the same direction it was going pre-absorption. This is just because the probability of a photon emission is always 50/50 regardless of where the emission occurs in the atmosphere.

“What’s important is how much the surface temperature and the temperature of the rest of the atmosphere has to increase to restore radiative balance at the TOA again. That’s about 1.2 K for the Planck feedback alone. Any increase in specific humidity will increase that value. The sign of cloud cover feedback is uncertain. Any reduction in the average land and sea ice cover will be a positive feedback.

Specifically, a ghg forcing of 3.6 W/m² at the TOA is supposed to be equivalent to a reduction in albedo corrected solar radiation of 3.6 W/m², not 1.8 W/m². That’s the definition of forcing. Using the seasonal cycle to diagnose climate sensitivity only gets you the sensitivity for time scales less than six months. That’s going to be fairly close to the Planck feedback sensitivity.”

Let’s assume for this discussion that the 3.7 W/m^2 from 2xCO2 is equal that of solar forcing as you claim.

Now, the time rate of response is independent of the direction of the feedback, at least for water vapor and clouds which certainly operate on time scales less than months. They have to – otherwise they wouldn’t change over the seasonal cycle as the surface temperatures change. The only thing those hemispheric gain plots don’t account for ice albedo feedback on a global scale, but even by the IPCC’s own quantification this is a very small contribution even if the combined feedback from water vapor and clouds is strongly positive.

As I see it, the fundamental difference between White’s approach and the approach used in traditional climate science, as well as why it is apparently so difficult for those trained in atmospheric science to grasp, is that of the fundamental difference between the systems analyzer (or systems engineer) and the atmospheric physicist. The methods George White is using are specifically designed to strip the boundary between the surface and TOA down to net energy flow, as this is what ultimately matters in the system (any system). That is, if the surface temperature is to increase by ‘x’ amount, the energy input supplied to the surface has to increase by ‘y’ amount, etc. If you know or have a measure of, for the example, the surface temperature changes to the changes in energy input the system, you can determine the net feedback in response to those changes, independent of knowing and quantifying the specific physical mechanisms that establish the net feedback and response.

To quote White himself on his analysis:

“What I’ve done is apply the kinds of techniques I would use to reverse engineer a black box system. I don’t care how it’s implemented inside, all I care about is replicating the behavior at the ports (observables). It doesn’t matter where the individual feedbacks are coming from, the net result of all the effects can be measured.”

Are you familiar with and/or do you by chance know of an access to a non-pay link for Lindzen’s paper entitled “Climate Physics, Feedbacks, and Reductionism (and when does reductionism go too far?)”. I couldn’t find one with a google search. Lindzen was kind enough to send it to me free via email earlier this year. The reason is there is a diagram on page 4 of the paper with a downward directed yellow arrow designated as “Radiative Forcing = F”. I guess this is largely what led me to believe that the IPCC’s definition of RF was additional energy in the act of radiating back downward, which would mean if the RF from 2xCO2 is supposed to be 3.7 W/m^2 per the IPCC’s definition, the 3.7 W/m^2 would all be downward radiated power.

I can forward you or anyone the paper via email (I don’t think Lindzen would mind). I would be interested in your taking a look and what you might have to say about it – specifically, if you think I have misinterpreted it somehow. Or just what you think it is depicting.

That picture of Lindzen does not describe the defining situation of radiative forcing where CO2 concentration is doubled suddenly. The Lindzen picture corresponds to the realistic case where CO2 concentration increases gradually and the temperature profile of the troposphere changes together with the surface temperature. In this case the atmosphere warms so slowly that it takes little energy and almost the whole radiative imbalance warms oceans and surface.

The defining case of radiative forcing is different. In this case most of the imbalance is used in initiating warming of the atmosphere. That warming starts as a very rapid one but levels up soon. The defining situation is, however, the initial one with rapid warming of the atmosphere. In that initial state the net flux is much smaller at surface than it is at TOA.

You should note also that the Lindzen picture includes also convection and latent heat transfer. For the net radiative flux alone the picture is in the Lindzen case rather similar to the initial defining case.

Thank you for taking a look. I must say I don’t understand how you’re interpreting what is depicted there as being what you’re saying above. Are the blue arrows in Figure 2 (for a, b, and c) on the previous page not that of post albedo solar power? If not, then what are they depicting?

“The approximate non-divergence of flux is also the rationale for assuming that radiative forcing is acting at the surface in simple energy balance models.”

I interpret this as meaning downward directed or downward radiated like post albedo solar power. Again, maybe this is not correct, but this is a good example of what I mean when I said earlier that intepretations and descriptions seem to vary all over the climate science community.

I always interpreted ‘net (down minus up)’ as the fraction of LW newly absorbed that is downward re-radiated or downward directed by the atmosphere. Hence why it is supposed to be equal to solar forcing. It seems everyone here is saying this is not what it means. Instead it’s just means ‘minus up’ for LW and the ‘down’ applies to post albedo solar power? The language seems contorted and not at all clear as to what it means (at least to me).

One of the reasons I decided to engage in a discussion on this again is precisely because Dewitt agreed that the 3.7 W/m^2 was just the net absorption increase as GW initially describes it. Most people I’ve encountered, including Roy Spencer, says that part is not correct.

Lindzen’s Fig 2 presents three situations
a) balance before adding GHG
b) the situation used to define radiative forcing
c) the new balance when warming is complete and no forcing remains

The arrows of Fig. 3 represent the long period between b) and c), i.e the time when the troposphere has also settled to a near balance and the rate of heating is determined by the large thermal inertia of oceans. During this time we still have forcing, not the full initial forcing but what’s left when warming has already reached the slow phase.

His Fig. 4 is about warming of oceans and land during the same period that corresponds to Fig 3. and the comment you pick from the page of the manuscript that you have refers exactly to the point that Fig. 3 applies to the situation of Fig. 4. (The pages of the manuscript that you probably have don’t agree with the pages of the final article. Thus they are a bad reference to the content. I use numbers of the figures.)

I haven’t read the whole article and don’t have any plans to do that. I would expect that Lindzen presents these basic issues in full accordance with main stream views. He’s skeptical on main stream results concerning feedbacks and climate sensitivity but not on the basics as far as I know.

“I would expect that Lindzen presents these basic issues in full accordance with main stream views. He’s skeptical on main stream results concerning feedbacks and climate sensitivity but not on the basics as far as I know.”

Also, I never said or implied the ‘gain’ is controlling anything – only that it is giving a measure of the net effect of everything that occurs in between the surface and the TOA – both radiative and non-radiative (known and unknown). That is, as the incident solar energy and temperature each change, as depicted in the gain plots, the gain quantifies the net feedback in response to the changes – be it net negative (less than 1.6) or not positive (greater than 1.6).

Maybe the issue is the energy balance at the surface is the sum of all of the effects and their complex interdependencies. Indeed there is quite a degree of complexity, because on average the surface receives more direct radiative power from the atmosphere and Sun than it emits, but much of this direct radiative power is replenishing non-radiative power leaving the surface (primarily as latent heat and convection) but not returned, making it net zero energy flux entering the surface. My point is regarless of how it is ultimately manifested at the surface, the sum must be about 385 W/m^2 for 287K, which then is also the amount of power directly radiated from the surface.

The biggest and most important topic in climate science is in regards to the whole question of feedback and climate sensitivity when interpreting satellite data, right? That is, distinguising cause from effect (i.e. forcing from feedback). For example, papers by Spencer and Lindzen show that, according to them at least, when this is properly done using various types of lead/lag analysis, the data shows the net feedback acting on the system is negative instead of positive. Here is a summary of how I think George White’s approach in the above linked analysis accomplishes this more easily and much more definitively.

Here are the two plots of measured satellite data (ISCCP) from the Northern and Southern hemispheres from the above analysis. Each plot represents a 25 year average of measured data (1983-2008):

The first thing to take note of is the dimentionless ‘gain’ in these plots quantifies the same thing and has the exact same physical meaning as to how they define feedback in climate science. The ‘gain’ in the plots is the just the dimentionless ratio of the absolute surface radiative power to the post albedo incident solar power entering the system. The global ‘gain’ is about 1.6 (i.e. 385/239 = 1.61). The global average gain is also the ultimate origin of the so-called ‘zero-feedback’ response from a doubling of CO2 that I referred to earlier. For warming, a response less than the global gain indicates negative feedback and a response greater than the global gain indicates positive feedback.

As an example, let’s take the sensitivity results from Lindzen’s most recent paper (L&C 2011). Right or wrong, if the result is shared with the whole earth, he’s getting a global sensitivity of about 0.8C from 2xCO2, or a net negative feedback reduction of about 25% acting on the climate to temperature increases. +0.8C from a baseline of 385 W/m^2 (287K from S-B) = +4.4 W/m^2 net radiative power increase at the surface from a ‘forcing’ of 3.7 W/m^2, and 4.4/3.7 = a dimentionless gain of 1.19 , which is less than the global gain or ‘zero-feedback’ gain of about 1.6 (1.1C = 6 W/m^2; 6/3.7 = 1.6). The dimentionless ‘gain’ going down as the forcing and temperature goes up physically means and quantifies the exact same thing in regards to the net direction of the feedback and resulting temperature increase at the surface – be it net negative (less than 1.6) or net positive (greater than 1.6). I emphasize this point because it seems most everyone in the atmospheric science community doesn’t even seem to realize or recognize this.

In the both of the above plots (i.e. the two hemispheres), the output energy flux is nearly equal to the input energy flux, which means there is very little energy flow occuring between the two hemispheres and each is responding to its post albedo incident energy flux almost entirely independent of the other. The big advantage here is the surface temperature changes are unambiguously and overwhelmingly caused by the large changes in incident solar energy, thus there is no ambiguity or difficulty in distinguising cause from effect (i.e. forcing from feedback). Moreover, the range of surface temperature increase to post albedo incident energy increase in the both plots extends significantly above the current global average, and in each hemisphere the response of the system is to oppose the temperature increase above the current global average (i.e. a response incrementally less than the average gain, indicating incrementally stronger net negative feedback in response).

Since the so-called ‘forcing’ from 2xCO2 is supposed to be equal to post albedo solar power entering the system, when the incident post albedo solar power goes above about 240 W/m^2 in each hemisphere, this is essentially the same as the ‘forcing’ that would occur from a doubling of CO2. Hence the applicability of the gain and feedback in response in those plots to the sensivitity of 2xCO2. Take a look at these flux plots for reference, which show the post albedo incident energy (‘power in’) and LW flux out at the TOA (‘power out’) for each hemisphere:

The key point here is that by considering only the radiative boundary fluxes at the surface and the TOA, it automatically accounts for any and all of the the non-radiative flux that occurs in response in between the boundaries as well. That is, the dimentionless ratio of the surface radiative power to the post albedo incident solar radiative power provides a direct measure of the net effect of everything that happens in between the boundaries – both radiative and non-radiative (known and unknown).

So going back to the example from Lindzen’s paper, a global sensitivity of about 0.8C from 2xCO2 physically means that it effectively takes about +4.4 W/m^2 of additional surface radiative power to offset an additional radiative ‘forcing’ of 3.7 W/m^2 (i.e. to re-establish equilibrium with space; about 240 W/m^2 in and out). Or just that it takes about 4.4 W/m^2 of of addititonal surface radiative power to allow 3.7 W/m^2 of radiative power leave at the TOA. (*Or even that it takes a net increase in energy supply to the surface of 4.4 W/m^2 to allow 3.7 W/m^2 of radiative power to leave at the TOA).

Again if this is still not clear, consider that the so-called ‘zero-feedback’ Planck response of about 3.3 W/m^2 per 1C of warming is itself directly derived from the global dimensionless gain ratio of 1.6 (i.e. +1C = +5.3 W/m^2 from S-B; and 5.3 W/m^2/1.6 = 3.3 W/m^2).

The ultimate conclusion of the analysis is the sensitivity of the climate to 2xCO2 has an upper limit of only about 0.55C because there is no physical or logical reason why the system would respond to an additional 1.85 W/m^2 of GHG ‘forcing’ more powerfully than the original 99+% (about 240 W/m^2) already forcing the system from the Sun (i.e. 1.85 W/m^2 x 1.6 = 3 W/m^2 = 0.55C from S-B). If one can’t accept the halving of the 3.7 W/m^2, then the upper limit would only be about 1.1C.

“In other cases the mean free path is so long (hundreds of meters or more) that description as a diffusion process fails due to the finite (non-differential) temperature difference between the point of emission and point of absorption”.

(I take “path” to refer to the path over which a radiative flux is extinguished by the mass of radiatively-active molecules it encounters in transit). I don’t see why the path length would determine whether the flux is one-way or two-way. Extinction/absorption occurs progressively along the path, not all at once at the end of it. Energy progressively absorbed is thermalised by collision with other molecules, maintaining local thermal equilibrium. The increment of absorption per unit length of path progressively reduces reflecting declining density of the absorbing mass along the (vertical) path. Hence, the temperature of LTE is lower at the top of the path than at the bottom independently of the length of the path. If energy transport by diffusion applies for short path lengths why wouldn’t it apply for all path lengths?

Why is it necessary to introduce radiative energy transport through the atmosphere? Especially when doing so presses S-B, a multiple integration of the Planck function, into service for which it was not designed? Is it not the case that the Planck function derives from consideration of energy density in a cavity with solid walls characterised by large numbers of contiguous molecules, all radiatively-active, which together express a uniform temperature? If so, that template, I would submit, is not readily fitted to a parcel of air – no surfaces, non-uniform temperature, a trace only of radiatively-active molecules.

The Planck formula is applicable to all emission of radiation of material with a single temperature, be its solid, liquid or gas. The intensity of emission is determined by the product of the value given by the Planck formula and emissivity which in turn is a constant for a opaque material and calculable from a constant and the thickness of the layer for transparent material like gas.

If we wish to understand energy flows in the atmosphere we must include all significant forms of energy transfer, radiative energy transfer is one of them and must therefore be included in any full description.

I was referring to the mean free path because it’s value affects the validity of different approaches to calculate radiative energy transfer. The mean free path is the average distance between the point where a photon is emitted and where it’s absorbed. If it’s small enough the local temperature and density are very close to the same value at the point of emission and the point of absorption. In such a case radiative heat transfer can be calculated accurately using the diffusion equation which is derived based on such an assumption, when the assumption is not valid the diffusion equation is not valid either.

If the mean free path is very long most of radiation passes trough the whole atmosphere, only a small fraction gets absorbed and the intensity is not affected much by the absorption. These two extreme cases are easy to calculate.

The calculation gets more complicated in the intermediate case where neither of the assumptions of very short or very long mean free path is true. That’s the case for many wavelengths of IR in the atmosphere. Doing proper calculation at those wavelengths requires sophisticated tools, i.e. computer programs like MODTRAN or some other of these.

“In terms of these macroscopic variables heat flows along temperature gradients from warmer to colder, but that refers only to the net sum of all the microlevel transfers that go in all direction”.

Is it not the case that:

*Micro-level, non-directional energy transfers are exchanges between molecular kinetic energy and electromagnetic energy of the “photon soup”/”wave field” which everywhere surrounds each and every molecule?

*Molecular vibrations and rotations result from either collisions with other molecules or interactions with EM photons/waves?

*The former (collision) case results in a unit of kinetic energy being converted to an equal quantity of EMR; and vice versa in the latter case?

*The net result of these individual micro energy exchanges being zero, the macro result in a parcel/slab/layer of atmosphere is also zero?

If these be true, do they not imply that micro-level energy transfers have no bearing on the temperature gradient nor, therefore, on the direction of energy fluxes, whether two-way or one-way? The (radiative) temperature gradient, my other post today argues, reflects reducing density of absorbing mass with altitude.

The net effect of the micro-level processes is not zero when the system is not in thermal equilibrium, i.e. when the temperature is not constant.

The average energy of molecules is higher in higher temperature. Those molecules that happen to move from warmer towards colder carry on average more energy than those moving in the opposite direction. (This is heat conduction:)

A warmer region of atmosphere emits more photons than a colder of the same mass. Therefore more photons happen to go from the warmer region to the colder one than in the opposite direction. That results in net energy transfer from warmer to colder, but photons do go in both directions. If the temperatures are not highly different the total amount of radiation emitted and absorbed is much larger than the net energy transfer.

What you appear to be forgetting is that at the TOA, there is no downward LW radiation. Even at the tropopause, there isn’t much downward radiation. MODTRAN tropical atmosphere clear sky:
17km looking down 289.037 W/m² (100-1500 cm-1)
17 km looking up 9.47 W/m²
Only 8.7% of that upward flux is absorbed by the atmosphere above 17 km.

You assume that local thermodynamic equilibrium is valid within a layer, but not between layers. The assumption of LTE within a layer isn’t strictly correct either, but the error is small and gets smaller as the layer thickness is decreased. At some point, it’s small enough to be ignored. Each layer emits equal fluxes up and down, but in the troposphere where most emission occurs, the layer below is warmer and emits more while the layer above is colder and emits less. Also, unlike an opaque sheet, each layer only absorbs a small fraction of the radiation impinging on it. The result is that there is a net flux upward.

Funny that you should say this, as the IPCC’s definition of RF is all that of downward radiated power (i.e. “net (down) minus up irradiance” and not ‘minus up irradiance’).

Correct. But at the TOA or the tropopause after the stratosphere is allowed to equilibrate, downward flux hasn’t change so the forcing is, in fact, the net reduction in upward radiation.

All he’s saying, independent of the reasons why he’s saying it (for which I don’t want to get into), is that upon its initial re-radiation by the atmosphere, half of the newly absorbed energy will be radiated back up in the same direction it was going pre-absorption. This is just because the probability of a photon emission is always 50/50 regardless of where the emission occurs in the atmosphere.

No, that’s not what he is saying. He’s reducing the forcing from 3.6 W/m² of CO2 forcing to 1.8 W/m² of solar forcing. That’s how he calculates a temperature change at the surface of 0.6 K instead of 1.2 K. And he’s wrong.

According to HITRAN based simulations, the atmosphere captures 3.6 W/m² of additional power when the CO2 is increased from 280ppm to 560ppm. Of this, the atmosphere radiates half of this up and half down. When the 1.8 W/m² of forcing power directed down is treated the same as 1.8 W/m² of additional solar forcing…[my emphasis]

Look at it another way, if only 1.8 W/m² is radiated upward, there is still a net reduction of upward radiation at the TOA of 1.8 W/m². That’s GW’s fundamental error. The rest of his and your analysis isn’t worth my time to dissect.

I’m afraid I just no longer have the mental energy to get into this to the degree necessary to explain it. Nice to know though you’re apparently absolutely certain you understand it and that he’s wrong.

“The rest of his and your analysis isn’t worth my time to dissect.”

Sorry for wasting your time then. A shame because if there are no errors in the plotting and processing of the data, I think he’s come about as close to absolute proof as possible that the net positive feedback and magnitude of warming predicted (3C or more) can’t happen. I guess your not alone though, as even stauch skeptics like Roy Spencer and others apparently can’t understand or grasp his methodology it either. It appears George has everyone on both sides totally faked out. A crying shame, IMO.

You should consider that when a lot of smart, educated people don’t take GW’s analysis seriously, it may not be that the analysis is too profound to be understood by the hoi polloi, it’s that it’s garbage and you’re the one being faked out.

When I see an egregious error in a paper I stop paying attention to it. I pointed out this error to you, and you continue to ignore it. A reduction in upwards emission of 3.6 W/m² from ghg forcing is equal to an increase of 3.6 W/m² of albedo corrected solar absorption, not 1.8 W/m². That error is fundamental to GW’s analysis. Whatever else he may have done correctly is irrelevant.

“You should consider that when a lot of smart, educated people don’t take GW’s analysis seriously, it may not be that the analysis is too profound to be understood by the hoi polloi, it’s that it’s garbage and you’re the one being faked out.”

Actually, I have considered this – multiple times even. Unfortunately, after more than two years and numerous discussions with many on both sides, I’m forced to conclude otherwise. With all due respect to all those ‘smart, educated’ people, I think they genuinely don’t understand it.

“When I see an egregious error in a paper I stop paying attention to it. I pointed out this error to you, and you continue to ignore it. A reduction in upwards emission of 3.6 W/m² from ghg forcing is equal to an increase of 3.6 W/m² of albedo corrected solar absorption”

Equal in what way? I certainly agree on W/m^2 it is equal, but I think you’re not considering that post albedo solar forcing is all downward radiated power, where as newly absorbed upward flowing radiation, when re-emitted, isn’t all downward radiated. Either the IPCC’s definition of RF is all downward radiated power or it isn’t. If it is, then if 3.7 W/m^2 is the ‘radiative forcing’ for 2xCO2 per the IPCC’s definition, then all of the 3.7 W/m^2 would have to be downward radiated power. If the calculated 3.7 W/m^2 is only the instantaneous net absorption increase, then all of this cannot be considered to be downward radiated power, because not all of what’s absorbed is downward re-radiated.

“That error is fundamental to GW’s analysis. Whatever else he may have done correctly is irrelevant.”

Well again, I’m glad you’re apparently absolutely certain he is wrong, as I’ve spent over two years investigating this in more detail than you can imagine and feel forced to accept that White, as best as I’ve been able to tell, is correct on this. Maybe I’m wrong though.

Put in the simplest way I can think of, the way the IPCC has applied the 3.7 W/m^2 net absorption increase to their definition of RF, they are effectively saying the following:

“According to HITRAN based simulations, the atmosphere captures 3.7 W/m² of additional power when the CO2 is increased from 280ppm to 560ppm. Of this, the atmosphere radiates 0% of this up and 100% down. When the 3.7 W/m² of forcing power directed down is treated the same as 3.7 W/m² of additional solar forcing….”

(*Also, here I said:“I certainly agree on W/m^2 it is equal”
What I meant was on an energy quantitative basis they are certainly equal.)

“According to HITRAN based simulations, the atmosphere captures 3.7 W/m² of additional power when the CO2 is increased from 280ppm to 560ppm.

True.

Of this, the atmosphere radiates 0% of this up and 100% down.

Not true. You have the initial state after an instantaneous doubling of CO2 and the final steady state. The path from initial to final isn’t the issue here. For the initial state, you are correct that 0% of the forcing is radiated upward. That, after all, is the definition of forcing. But you are wrong about 100% down. Instantaneously, the increase in downward radiation is much less than 3.7 W/m². That’s because the temperature of the atmosphere hasn’t changed yet. At the new steady state, 100% is radiated upward. If it weren’t, there would still be a radiative imbalance and no steady state. At the surface, the downward radiation has increased by more than 3.7 W/m². How much depends on the total of all the feedbacks.

When the 3.7 W/m² of forcing power directed down is treated the same as 3.7 W/m² of additional solar forcing….”

For an increase in solar forcing, emission at the TOA has to increase by the amount of the increase in solar absorption at the new steady state. For no feedback other than Planck, the surface temperature increase is almost identical for the same change in forcing.

You don’t really understand how the greenhouse effect actually works. Neither does GW. I think his and your problem is the half up, half down thing that kept you from understanding that the TFK09 energy balance numbers really do add up.

If all the energy absorbed by the atmosphere and the surface were immediately radiated away in any direction, the atmosphere and the surface wouldn’t warm. Both have a non-zero heat capacity. The energy content of the atmosphere and the surface must therefore increase to increase the temperature. That means by definition less energy will be radiated than absorbed until the new steady state is reached. That’s true whether TOA emission is reduced or absorption is increased. Heat transfer 101.

You’re getting way ahead of me here. It’s my understanding that so-called ‘radiative forcing’ of climate via GHGs (and its quantification) is that of an increase in radiative resistance to cooling. Specifically, that is, the additional absorption of radiative energy that was prior all acting to cool by passing into space that is subsequently re-radiated back downward upon its initial re-radiation by the atmosphere (*the re-radiation back downward can be from either ‘spotaneous’ emission if the absorbed energy is thermalized or from ‘stimulated’ emission if the absorption of photon cause the emission of another). By this definition, the amount of newly absorbed energy that is subsequently radiated back up in the same direction it was going pre-absorption is not increasing radiative resistance to cooling and is thus not acting to warm, at least not in the same way as post albedo solar power, which is all downward radiated (that is, continuously downward radiated in).

Do you NOT agree that the IPCC’s definition of ‘radiative forcing’ is all that of downward radiated power? And that this is the reason why, at least on W/m^2, the ‘forcing’ is considered to be equal to that post albedo solar power, which is all downward radiated?

If so, then on what physical basis is the ‘forcing’ is considered to be equal that of solar forcing? This is what I do not understand and cannot reconcile.

You seem to talking about what happens in the atmosphere post the initial ‘forcing’. That is, after the newly absorbed energy is downward re-radiated and has increased radiative resistance to cooling. This is entirely separate from the actual quantification of the initial ‘forcing’, which is at the core of the disagreement, and what White is claiming.

By this I mean surely you agree that 1.85 W/m^2 of GHG ‘forcing’ per the IPCC’s definition yields a ‘zero-feedback’ warming of only 0.55C, and the same is the case for 1.85 W/m^2 of additional post albedo solar forcing.

Let’s review the IPCC’s definition:

“the change in net (down minus up) irradiance (solar plus long-wave; in Wm-2) at the tropopause AFTER allowing for stratospheric temperatures to readjust to radiative equilibrium, but with surface and tropospheric temperatures and state held fixed at the unperturbed values.”

First of all, this is an incredibly convoluted way to define a forcing. That aside:

To me, the use of the word ‘net’ in conjunction with “(down minus up) implies an amount subtracted from a gross quantity. If 3.7 W/m^2 is the gross quantity of newly absorbed energy (as you yourself acknowleged, much to my surprise), how can all of it be downward re-radiated by the atmosphere? As best I know, the probability of radiative emission up or down is always 50/50, and this is the case whether the emission occurs 1 inch from the surface or 1 inch from the TOA.

Maybe I’m missing something, but this doesn’t add up and make sense to me. Mind you, I’m fully aware that the atmosphere directly radiates more power to the surface than it does out the TOA, but this is due primarily to the lapse rate – not because the atmosphere anisotropically radiates its energy.

Also, as I understand it the calculation of ‘zero-feedback’ is not really a heat transfer calculation in the traditional sense, because it assumes all the other heat/energy transfer elements are held fixed.

Also, just to clarify, all White means when he says “Of this, the atmosphere radiates half of this up and half down….” is that upon the initial re-radiation of the newly absorbed energy, basic physics dictates that half will be radiated back down while other half will be radiated back up in the same direction it was going pre-absorption. That’s it. Nothing more.

I think this is being misinterpreted as him saying (or implying) that half of the newly absorbed energy is subsequently directly radiated to the surface and half is directly radiated into space (i.e. in one ‘pass’). This is definitely not the case, as in either scenario the energy can be subsequently absorbed, thermalized and re-radiated again multiple times – each time with a 50/50 probability of going up or down. As a result, that which is initially re-radiated back up can find its way re-radiated back down and vice versa. Eventually though, all of absorbed energy must either find its way radiated to space or to the surface in some form.

It’s my understanding that so-called ‘radiative forcing’ of climate via GHGs (and its quantification) is that of an increase in radiative resistance to cooling. Specifically, that is, the additional absorption of radiative energy that was prior all acting to cool by passing into space

Good so far.

that is subsequently re-radiated back downward upon its initial re-radiation by the atmosphere

No. There is no such thing as re-radiation. Throughout most of the atmosphere, energy transfer from an excited molecule by collision with another molecule is several orders of magnitude more likely than by emission of radiation. So there is emission and absorption. Emission is a function of the number of molecules in an excited state which in turn is a function of temperature and concentration. Absorption is a function of concentration. Temperature can affect absorption but only second order through Doppler and pressure line broadening. Emission is going to happen whether there is absorption or not. Emission and absorption of energy at a given altitude are only equal at steady state if there is no other source of energy. In the troposphere, convection from the surface is a significant source of energy and emission exceeds absorption. If absorption increases but emission doesn’t or increases less, then energy accumulates and the temperature goes up until steady state is restored by the increased emission at higher temperature, and conversely. The radiative balance at the TOA affects whether energy is accumulating or not. The effect of energy accumulation at the surface depends on a lot of things like the environmental lapse rate and the specific humidity.

This seems to be the crux of the disagreement. I do not understand how ‘there is no such thing as re-radiation’ of the absorbed energy by the atmosphere. I do understand that the absorbed energy can be thermalized via collision, but the thermalized gases in the atmosphere radiate their accumulated energy like any other heated object, do they not?

“A reduction in upward LW radiation is almost exactly equivalent to an increase in absorbed downward SW radiation in terms of the change in surface temperature necessary to restore radiative balance. That’s the physical basis that you’ve somehow managed to miss.”

I know this is what is claimed (arbitrarily to me), but I do not understand the physical why if not all of the absorbed energy will be downward re-radiated by the atmosphere, where as post albedo solar power is all continuously radiated down in.

Do you NOT agree that the IPCC’s definition of ‘radiative forcing’ is all that of downward radiated power? And that this is the reason why, at least on W/m^2, the ‘forcing’ is considered to be equal to that post albedo solar power, which is all downward radiated?

No. I do not agree. The IPCC’s definition of forcing is the net radiative flux at the tropopause after the stratosphere is allowed to reach steady state, down minus up. The stratosphere is allowed to relax because the time constant for that relaxation is weeks to months while the lower atmosphere and surface takes centuries or longer to reach steady state. A reduction in upward LW radiation is almost exactly equivalent to an increase in absorbed downward SW radiation in terms of the change in surface temperature necessary to restore radiative balance. That’s the physical basis that you’ve somehow managed to miss.

The so-called stratospheric adjustment is only a tiny fraction of the 3.7 W/m^2. It’s net adjustment of less than 0.1 W/m^2. Myhre himself told me that the 3.7 W/m^2 net absorption increase can be considered that which occurs through to the TOA, because the arrived at 3.7 W/m^2 figure includes the stratospheric adjustment.

So the application of the 3.7 W/m^2 to the IPCC’s definition still doesn’t make sense to me. What amount of the 3.7 W/m^2 has been subtracted for the ‘minus up’ portion if all of the 3.7 W/m^2 is then ‘net down’ (since 3.7 W/m^2 is the quantification of RF per the IPCC’s definition for 2xCO2)?

RW: I’ve read some of your exchanges with DeWitt. The following may help. As I understand things, radiative energy flux is not conserved when radiative forcing is calculated. After doubling carbon dioxide, calculations indicate that 3.6 W/m2 less radiation passes upwards through the tropopause, but this “missing” radiation isn’t traveling downward or in some other direction. The “missing radiation” is being converted to heat (conserving energy) that will slowly warm the land, ocean and lower troposphere. Eventually these bodies will warm enough so that upward flux of LWR through the tropopause will be restored to pre-doubling levels. However, we calculate radiative forcing BEFORE any of this future warming has occurred.

Many people say that the greenhouse effect arises because CO2 in the atmosphere intercepts upward LWR and redirects it in all directions; with a 50% chance of going up and a 50% chance of going down. This interpretation makes “re-direction” behave like scattering. Absorbed LWR is not being scattered; scattering and absorption are totally different processes. Absorption is usually followed by collisions that turn radiation into the kinetic energy of motion of gas molecules. This process (thermalization) is much faster than re-emission. Absorbed energy CAN reappear as radiation, but only through the emission term (second term) of the Schwartzschild equation (shown for a non-scattering atmosphere):

dI/ds = -noI + noB(T)

where I is radiation flux in a particular direction at a particular wavelength, dI/ds is the incremental change in radiation flux (dI) along an incremental path length (ds), n is the number of absorbing/emitting molecules per unit volume, o is the absorption/emission cross-section and B(T) is the Planck function for that wavelength. Notice that emission at a particular wavelength is NOT directly controlled by how much radiation has been absorbed; it is controlled only by temperature (through the Planck function, B(T). If a large amount of radiation passes through a very cold gas, that gas will absorb a lot of radiation and emit very little. Eventually the difference between absorption and emission will cause this very cold gas to warm; but until warming is complete, the amount of radiation redirected downward will not be equal to half of the upward radiation absorbed!

The radiative forcing for 2X CO2 is calculated BEFORE the energy absorbed by the extra carbon dioxide has had a chance to change the temperature of the troposphere. This procedure is used because we can’t predict how radiation will change the temperature of a particular location in the troposphere – temperature in the troposphere is mostly controlled by convection. So radiative forcing is calculated assuming a fixed temperature profile for the troposphere and surface (that hasn’t yet responded to changed absorption and emission).

(Since vertical convection is unimportant in the stratosphere, we can predict how changes in GHGs will change radiation and will change the temperature of the stratosphere. So the IPCC allows temperature in the stratosphere to respond to changes in radiation, but not the troposphere.)

I appreciate your detailed explanation, though I’m not sure I understand it relative to what Dewitt and I are debating/discussing, which is the equivalency of a net absorption increase of 3.7 W/m^2 to that of 3.7 W/m^2 of additional post albedo solar forcing, as well as how it specifically relates to the IPCC’s definition of RF and its supposed equivalency to post albedo solar forcing.

Here is summary of my understanding of the fundamentals involved, which may help:

When CO2 is doubled, surface’s ability to cool by directly radiating to space is reduced by about 3.7 W/m^2. That is, the atmosphere absorbs an additional 3.7 W/m^2 of surface radiative power that was previously passing straight through to space (the same as if the atmosphere wasn’t even there). This in turn then requires the atmosphere and ultimately the surface to warm in order to re-establish equilibrium with space. Now, I do not understand how these generally established basics support the notion that the 3.7 W/m^2 net absorption increase is equal to that of post albedo solar power (specifically in its ability to act to ultimately warm the surface). This is primarly for two reasons:

1. Not all of the newly 3.7 W/m will be downward re-radiated by the atmosphere, where as 3.7 W/m^2 of additional post albedo solar power is all downward radiated in (i.e. continuously acting to warm).

2. The energy radiated from the surface absorbed by the atmosphere has the potential to leave the atmosphere over twice the area it arrives from. That is, in the from bottom initially (the surface), but out the top or bottom.

1. Not all of the newly absorbed 3.7 W/m will be downward re-radiated by the atmosphere, where as 3.7 W/m^2 of additional post albedo solar power is all downward radiated in (i.e. continuously acting to warm).

Here is summary of my understanding of the fundamentals involved, which may help:

When CO2 is doubled, surface’s ability to cool by directly radiating to space is reduced by about 3.7 W/m^2. That is, the atmosphere absorbs an additional 3.7 W/m^2 of surface radiative power that was previously passing straight through to space (the same as if the atmosphere wasn’t even there)..

Your understanding is not correct.

The surface and the atmosphere have a reduced ability to cool. The OLR is the sum (vertically integrated) of all levels from the surface through to the top of atmosphere.

What the satellites measure is radiation from the surface, from the atmosphere 1km up, from the atmosphere 2km up, etc.

Increases in GHGs reduce this OLR. There is absorption and emission at all levels within the atmosphere.

When we do the calculation of radiative transfer we find that doubling CO2 from pre-industrial levels reduces the emission of radiation that appears at the top of atmosphere (the OLR) by 3.7 W/m2.

According to Gunnar Myhre and George White, who have both done the calculation themselves from scratch (White from the latest HITRAN spectral data), and who I have sought direct clarification with on this, the 3.7 W/m^2 is all that of surface radiative power newly absorbed by the atmosphere (i.e. the calculation specifcally does not include reduction in emission of radiative power that originates from the atmosphere itself). It is the sum of absorption of surface radiative power through the number of layers the atmosphere is divided into for the RT simulation.

However, even if it does include reduction in emission from the atmosphere itself, the atmosphere would still none the less radiate half of this back up in the same direction it was going pre-absorption. So relative to the fundamental issue in contention, this wouldn’t seem to matter.

The whole point is the IPCC’s definition of RF is specifically that of power in the act of radiating downward and not in the act of absorbing. This is the crux of the issue.

According to Gunnar Myhre and George White, who have both done the calculation themselves from scratch (White from the latest HITRAN spectral data), and who I have sought direct clarification with on this, the 3.7 W/m^2 is all that of surface radiative power newly absorbed by the atmosphere (i.e. the calculation specifcally does not include reduction in emission of radiative power that originates from the atmosphere itself). It is the sum of absorption of surface radiative power through the number of layers the atmosphere is divided into for the RT simulation.

I believe I’ve done this before, but I’ll do it again. For the US standard atmosphere, the average transmittance at 280 ppmv for clear sky conditions from 100-1500 cm-1 is 0.2551. Increasing the CO2 to 560 ppmv reduces the transmittance to 0.2492 for a difference of 0.0059. The surface radiates 360.472 W/m² at 288.2K. That puts the reduction in transmitted power from the surface at 2.13 W/m² while the reduction in emission at the tropopause is 3.42 W/m². For the tropical atmosphere, it’s even less at 1.04 W/m² increased absorption and 4.49 W/m² decreased emission. It’s also true for a cloud covered sky, but the difference is smaller. I don’t know about Myhre, but I wouldn’t trust George White to make change at a fast food restaurant. Whatever, they’re both wrong.

The whole point is the IPCC’s definition of RF is specifically that of power in the act of radiating downward and not in the act of absorbing. This is the crux of the issue.

No, it isn’t. You’ve quoted the IPCC’s definition above and it doesn’t say that. The IPCC’s definition is specifically that the magnitude of radiative forcing is the flux imbalance, down minus up, at the tropopause after the stratosphere is allowed to reach steady state. Whether it’s a reduction in upward radiation or an increase in downward radiation doesn’t matter to the calculation. That isn’t the same as your statement of the IPCC’s definition of radiative forcing at all. As I’ve said before, you don’t really understand. You have adopted several incorrect ideas as being correct and they distort everything else you look at. Because you can’t reconcile those wrong ideas with what most scientists believe, you think they must be wrong. But that’s usually never true. You need to start from scratch. Unlearning bad habits or ideas is tough, though. The first step is to admit to yourself that you’re wrong. Until you do that, you’ll never make any progress.

No, I do not understand, as it just genuinely does not make sense to me. No where in the IPCC’s definition is there any mention of a ‘flux imbalance’. Moreover, what does ‘down (minus up)’ mean specifically? What is ‘down’ and what is ‘(minus up)’. What are their quantifications and whas the basis for their quantifications? The whole point is the 3.7 W/m^2 of net absorption increase is just plain ‘minus up’ (i.e. the instantaneous reduction of outgoing LW at the TOA upon a doubling of CO2). How does this become ‘net down (minus up) irradiance’?

No, I do not understand, as it just genuinely does not make sense to me.

That’s obvious.

What is ‘down’ and what is ‘(minus up)’. What are their quantifications and whas the basis for their quantifications?

Easy. Take disk with emissivity =1 and insulate it. At the TOA that would mean making the back side have as low an emissivity as possible. Orient the disk so that the perpendicular is parallel to a line from the disk to the center of the earth. The temperature of the disk can then be used to calculate flux from the Stefan-Boltzman equation like a precision spectral pyranometer (PSP). When the black surface is pointed toward space, you’re measuring total flux down. When it’s pointed towards the Earth, you’re measuring flux up. For flux up, you have to shield the disk with a hemisphere that reflects SW radiation and passes LW radiation, in other words, it’s a pyrgeometer or precision infrared radiometer. To correct for albedo you need another PSP pointed down to measure reflected SW radiation. The difference between incident and reflected SW is the albedo corrected downward flux. The downward flux averaged over a year and the entire planet is ~239 W/m². According to TFK09, the global annual average upward flux is 238.1 W/m² creating a net forcing of 0.9 W/m², 239-238.1 = 0.9, down – up. The forcing can increased if downward SW flux increases from 239 W/m² or if LW upward flux decreases from 238.1 W/m².

The whole point is the 3.7 W/m^2 of net absorption increase is just plain ‘minus up’ (i.e. the instantaneous reduction of outgoing LW at the TOA upon a doubling of CO2). How does this become ‘net down (minus up) irradiance’?

Because down hasn’t changed. The assumption is that before the industrial revolution the net forcing was zero and the incident solar forcing hasn’t changed very much, meaning that the LW flux was also 239 W/m². If we then double CO2 instantaneously from the pre-industrial level, the upward flux would be instantaneously reduced to 235.3 W/m² causing a flux imbalance and a net forcing of 3.7 W/m², 239 – 235.3 = 3.7. The global average of 3.7 is calculated by integrating over the whole planet using radiative transfer calculations based on local conditions. See http://i165.photobucket.com/albums/u43/gplracerx/2xCO2globalforcing.jpg from Hansen, et.al. (2005).

If the net forcing is positive then energy must be accumulating somewhere and temperatures somewhere are going up. For example, we know that ocean heat content is increasing from ARGO data and the XBT’s used before that. But ARGO only measures the top 2000m of the ocean and it hasn’t been going long enough to be sure all the bugs in the system have been found and eliminated. So it hasn’t been possible to determine the accuracy of the calculated net forcing. The observations from space also have precision problems.

RW: Thanks for the reply. It seemed to me that you may have been interchanging the concepts of scattering with re-direction of absorbed OLR. I was under the illusion you thought the extra OLR absorbed by doubled CO2 must be re-radiated in all directions. The amount of OLR re-directed downward by GHGs depends on the temperature of the GHGs, not how much OLR they absorb. The radiative forcing calculation doesn’t allow the troposphere to warm, so the extra energy absorbed by CO2 seems to “disappear” rather than show up as re-directed radiation.

As for the equivalence of solar and GHG forcings, the photons that will eventually carry away the extra energy from both forcings will be emitted from roughly the same location in the upper troposphere. That location must warm about the same amount to restore radiative balance. No matter where the forcing initially deposits extra radiation, heat must flow from that site to the upper troposphere. If one believes the atmosphere is well mixed by convection (by the Hadley circulation for example) and that the mean global environmental lapse rate is constant, perhaps the surface warming from the two forcings will be the same. If the extra heat from one forcing must be “driven” to the upper troposphere by a steeper lapse rate, the surface warming may differ.

The biggest difference I can see is that DLR from forcing by GHGs is deposited in the top mm of the ocean whereas increased solar is deposited mostly in the top 10 m. The solar energy can’t reach the surface until night, when radiative cooling at the surface permits denser surface water to sink and solar-warmed water to rise.

Also, I think most of the GHG molecules in the atmosphere are in a high enough energy state where the probability of ‘stimulated’ emission upon absorption is very likely. In this case, re-emission would happen virtually instantaneously, always with a 50/50 probability of going up or down.

When CO2 is added suddenly to the atmosphere but the temperatures have no time to adjust (as is assumed for the troposphere in the IPCC definition of radiative forcing) the immediate effect is an increase in the emission and opacity due to absorption at every point of the atmosphere. For every small volume (dimensions less than 1m) both changes are proportional to the change in concentration. For larger volumes the proportionality is not true due to beginning saturation of absorption and absorption of part of the emitted radiation within the volume. In particular the proportionality is not even close of being true for the entire troposphere.

What happens for radiation up from the top of the troposphere is a combination of increased emission from layers close to the top and reduction of radiation from lower atmosphere and surface due to increased opacity of the atmosphere. The reduction due to increased opacity wins because temperature decreases with altitude. The total estimated amount of 3.7 W/m2 for doubling of CO2 is mostly due to changes in radiation originating within the atmosphere and only for a minor part due to reduced transmission of radiation from the surface. In other words radiation directly from the surface to space decreases much less than 3.7 W/m2.

The radiation from the surface does not change at all as the surface does not change by the increase of CO2. As the down-welling radiation from the atmosphere increases there will be an decrease in the net LWIR from the surface, but there’s no reason for this increase to be equal to the decrease of net radiation up at TOA. The difference of these changes will initiate warming of the troposphere, because it turns out that the change at the surface is smaller than at the top of troposphere. The calculation of the actual numbers requires a full description of the state of the atmosphere and the use of a radiative code like MODTRAN.

Thanks for that. Given the provenance of the Planck formula and the very different states of matter expressed in solids and gases, some explanation of how the formula applies equally to both states would be useful if not mandatory to an understanding of atmospheric heat transfer, IMO. Any references?

Would two gases, one pure CO2, the other pure N2, in the same thickness slabs and at the same temperature radiate with equal power?

The Planck formula works with a constant temperature which in the atmosphere exists only in the surface layer and at the tropopause. Applying it in the rest of the troposphere requires applying it to thin slices where an approximation to a constant temperature can be made. In a thin slice, isn’t the mean free path of necessity short where (you say) calculating energy transport by diffusion, which is far simpler than by radiative transfer, is acceptable? Why forego the simpler calculation for the complex one?

and trough the link to atmospheric radiation in the roadmap in the top section of his links. Perhaps you find the answer in those posts but my impression is that some introductory sections would still be needed. SoD might be able to tell where such basic description is presented.

I looked also to Wikipedia but didn’t find exactly the right material there either, although it would fit well to the idea of Wikipedia. Writing it well would take more effort than I’m ready to spend right now.

Concerning MODTRAN I have understood that it uses 33 (or 34 I’m not sure of the exact values) layers of varying thickness to cover the Earth atmosphere up to 100 km altitude. Using such a number of layers means that absorption within the layer must be taken into account for emission as well as saturation of the absorption at wavelengths with strong absorption.

It’s 33 including the surface and goes to 100km. And yes it does calculate emission based on the optical depth for each frequency band of 2 cm-1 from 100-1500 cm-1 using a band model rather than line-by-line. I’ve compared MODTRAN data to line-by-line and it’s pretty close and takes a lot less time. You don’t need to have layers that are optically thin at all frequencies. You just have to have enough that adding more layers doesn’t make a significant difference.

Click on ‘submit the calculation’ then scroll to the bottom of the graph frame and click on ‘View the whole output file’. I don’t think you need to select save the text for later retrieval. The data seems to be there anyway, and there’s lots of it. One thing that’s a little tricky is that some of the atmospheric concentrations are expressed as path lengths, atm cm/km. That’s the length in centimeters at one atmosphere of the component gas in a 1 km layer if it were separated from the other gases. Obviously all the components have to add up to 1 km/km.

Concerning the sum of the atm-cm/km values it’s more complete to say that they add to 1 km/km at the surface and to smaller value proportional to the density at higher altitudes. The density is in turn proportional to p/T (pressure/temperature).

Correct. They do add to the correct total for the full atmosphere column, ~300 cm for CO2 at 375 ppmv for example. I’ve been round and round with Nasif Nahle over the years on that one. But then I’m still not sure has has accepted the fact that a column of air reaching to the top of the atmosphere with a surface area of 1 m² weighs ~10,000 kg.

To answer your question, N2 is almost perfectly transparent in the thermal IR frequency band so it would radiate orders of magnitude less radiation than a similar amount of CO2, which is far from transparent.

“Increases in GHGs reduce this OLR. There is absorption and emission at all levels within the atmosphere.”

I understand this. The question is does the calculated 3.7 W/m^2 per CO2 include reduction in emission from the atmosphere itself or is it specific to surface radiative power newly absorbed through all the levels within the atmosphere? If it is all specific to surface radiative power newly absorbed, this would still raise the effective average emission level to a cooler level, thus creating an imbalance none the less.

My understanding is the 3.7 W/m^2 is the sum of the net absorption increase of surface radiative power through all the layers the atmosphere is divided into for the RT simulation. For example, if the atmosphere were divided into 4 layers and the net absorption increase of surface radiative power per layer was 1 W/m^2 through layers 1, 2 & 3, and 0.7 W/m^2 through layer 4, the total net absorption increase through the whole atmosphere would be 3.7 W/m^2. I know these numbers for the individual layers are not correct, but if they were, this is how it works.

Now, I most certainly agree that upon an ‘instantaneous’ doubling of CO2, a reduction in radiation to space emitted from the atmosphere itself would also occur, but so too would a reduction in radiation from the atmosphere to the surface occur at the same time. These essentially cancel one another out or are not considered in the calculation. Since in the former case, this energy has already been prior absorbed from radiation from the surface (or Sun), or from non-radiative energy moved from the surface into the atmosphere, it doesn’t reduce the surface’s ability to cool by directly radiating to space, and thus doesn’t enhance the GHE.

Again, maybe this is wrong, as I’ve never done these simulations myself and don’t really even know how to. White, who has done the simulation himself says when he doubles CO2 it results in decrease in flux going out to space of about 3.7 W/m^2 that is uninfluenced by GHGs and a corresponding 3.7 W/m^2 increase in surface radiative power absorbed by the atmosphere. I should point out everyone I’ve encountered, including Roy Spencer, says this is wrong, but When Myhre, who is the standard reference for the figure in the literature, confirmed that the physical meaning of the 3.7 W/m^2 was exactly White claims it is, that convinced me White was correct. It seems those who disputed it have not actually done the calculation themselves from scratch.

I find it very troubling and quite frustrating that something as basic and fundamental as this has apparently multiple intepretations all throughout the climate science community, and that I apparently can’t get a straight and definitive answer in the exact physical meaning of the 3.7 W/m^2 per CO2 doubling. In many of the discussions I had with people, they even said that the net absorption increase should actually be 7.4 W/m^2 and that 3.7 W/m^2 was the downward re-emitted half, but of course no one could ever provide support.

“Again, maybe this is wrong, as I’ve never done these simulations myself and don’t really even know how to. White, who has done the simulation himself says when he doubles CO2 it results in decrease in flux going out to space of about 3.7 W/m^2 that is uninfluenced by GHGs and a corresponding 3.7 W/m^2 increase in surface radiative power absorbed by the atmosphere. I should point out that everyone I’ve encountered, including Roy Spencer, says this is wrong, but When Myhre, who is the standard reference for the figure in the literature, confirmed that the physical meaning of the 3.7 W/m^2 was exactly what White claims it is, that convinced me White was correct. It seems those who disputed it have not actually done the calculation themselves from scratch (or don’t really know what is actually being calculated and why).

“I find it very troubling and quite frustrating that something as basic and fundamental as this has apparently multiple intepretations all throughout the climate science community, and that I apparently can’t get a straight and definitive answer on the exact physical meaning of the RT calculated 3.7 W/m^2 per CO2 doubling. In many of the discussions I had with people, they even said that the net absorption increase should actually be 7.4 W/m^2 and that 3.7 W/m^2 was the downward re-emitted half, but of course no one could ever provide support.

Did GW compare the results of his ‘from scratch’ calculation to other established line-by-line programs like the free LBLRTM or the subscription program at spectralcalc.com? If he didn’t, then how can you possibly know that his calculations are correct? You say Myhre told you that it’s all absorption of surface radiation but you don’t seem to be able to provide confirmation of this communication

Did you read my post above where I used MODTRAN to do the calculations you blather on about so much? It’s very simple, the reduction in transmission of surface radiation to space is insufficient to explain the total reduction in emission. Period.

“Did GW compare the results of his ‘from scratch’ calculation to other established line-by-line programs like the free LBLRTM or the subscription program at spectralcalc.com?”

I don’t know.

“If he didn’t, then how can you possibly know that his calculations are correct? You say Myhre told you that it’s all absorption of surface radiation but you don’t seem to be able to provide confirmation of this communication.”

Post your email address and I’ll foward you the entire exchange I had with Myhre. I don’t feel completely comfortable posting it here for some reason.

“Did you read my post above where I used MODTRAN to do the calculations you blather on about so much? It’s very simple, the reduction in transmission of surface radiation to space is insufficient to explain the total reduction in emission. Period.”

Yes I did. I spent some time playing with that long ago. I could never rectify the text output with the web output, nor could I really understand exactly what it was doing with the calculations.

I spent some time playing with that long ago. I could never rectify the text output with the web output, nor could I really understand exactly what it was doing with the calculations.

You do know that you have just admitted that you don’t have a clue what you’re talking about. And yet you insist that not only do you know, but you know enough to reject what everyone else except one or two people who are clearly on the fringe are telling you. You should be asking questions and paying attention to the answers instead of ignoring everything that doesn’t fit your preconceptions like you did when discussing the KT97 and TFK09 energy balance.

Again, if you seriously want to understand how line by line and band radiative transfer programs work, buy and read carefully Grant Petty’s A First Course in Atmospheric Radiative Transfer. It’s all there. If you have a few specific questions about the MODTRAN text output, I may be able to answer them. But I suspect that you are not at a level yet where you would understand the answers.

I can confirm (I trust that the emails are genuine although I cannot confirm that) that Myhre answered by two words

Yes, correct.

to an email of RW, where RW presented similar views as here

Basically, the +3.7 W/m^2 of ‘net absorption increase’ from 2xCO2 is the reduction in the surface radiative flux passing directly into space at the TOA, right? Meaning when CO2 is doubled, the outgoing flux at the TOA reduces from 240 W/m^2 to 236.3 W/m^2 and the atmosphere absorbs and additional 3.7 W/m^2 of surface radiative power that was previously passing directly out the TOA the same as if the atmosphere wasn’t even there.

Do I finally understand it correctly?

My interpretation was and still is that Myhre misinterpreted the question. That’s obvious to me because the scientific papers of Myhre et al state the opposite and they have certainly been much more careful in writing the papers as in answering one particular email with two words. Just think how common it is that people write such short answers without reading carefully the question, when they don’t want to spend much time with an issue that seems to be of little importance.

I had an email exchange with RW (he sent me 20 messages and I back 19). That was equally unproductive as the discussion here. There just isn’t a way to get him accept valid physics.

It’s ridiculous that a short incoherent text of GW is supposed to be superior to the general understanding of physics written in textbooks read by innumerable students and confirmed by the consistent success in explaining all phenomena whenever it’s possible to compare the theory accurately with empirical data.

Post your email address and I’ll foward you the entire exchange I had with Myhre. I don’t feel completely comfortable posting it here for some reason.

I had a very long email exchange with RW on the basics of radiative transfer and the first law of thermodynamics that I finally stopped responding to.

However, RW did supply the email exchange to me from Myhre, and I feel quite comfortable placing here because Myhre understands radiative transfer extremely well and better to have his views clearly stated.

When someone understands as little as RW, yet with absolute certainty in his own capability in the field, it is pretty easy to eventually get a “yes” answer and not realize why..

————- Sat, 28 Jan 2012, RW wrote —-
I’m wondering if you can help me with a question. In this paper of yours on page there is a graph showing that the ‘radiative forcing’ from a doubling of CO2 (280-560ppm) is about 3.7 W/m^2.

Is the 3.7 W/m^2 the net absorption increase (i.e. the reduction in the direct surface to space transmittance)? If not, then what is the net absorption increase for 2xCO2?

————- Mon, 30 Jan 2012 10:19:32 ——————
Hi Randall,

The 3.7 Wm-2 for a doubling of CO2 concentration is the net change in the absorption at tropopause level. The tropopause level is more relevant for surface temperature changes than change in the fluxes at the surface. I do not have values for the surface, sorry.

Cheers,
Gunnar
————————————

[my emphasis added]

This is a precis of the standard IPCC description, which is very well understood by everyone in the field.

————– On Sat, 4 Feb 2012 02:23:36 RW wrote —-
Hi again Gunnar,

Just to be absolutely sure I understand the exact physical meaning of the calculated 3.7 W/m^2 per CO2 doubling, can you tell me:

Is the 3.7 W/m^2 the reduction in the direct surface transmittance to the tropopause? By ‘direct surface transmittance to the tropopause’ I specifically mean the amount surface emitted radiative power (all photons) that passes straight from the surface to the tropopause the same as if there was not even an atmosphere in between the surface and the tropopause?

In other words, when CO2 is doubled, an additional 3.7 W/m^2 of surface emitted radiative power (all photons) is absorbed by the atmosphere in between the surface and the tropopause that previously passed straight through to the tropopause?
——————————————

————– On Sun, 5 Feb 2012 20:10:24 —-

Hi,

The 3.7 Wm-2 is the change in the radiative flux (irradiance) at the tropopause (since stratospheric temperature adjustment is included this is the same at the tropoapause and top of the atmosphere). This change can be compared to the outgoing radiative flux at the top of the atmosphere of around 240 Wm-2. The absorption occur both in the troposphere and the stratosphere.

Cheers,
Gunnar
———————————————————————-

The same answer

—————On Tue, 7 Feb 2012 05:31:09 RW wrote——–
Gunnar,

Having re-read your response here I think you may have answered my question. Sorry if I missed it the first time.

Basically, the +3.7 W/m^2 of ‘net absorption increase’ from 2xCO2 is the reduction in the surface radiative flux passing directly into space at the TOA, right? Meaning when CO2 is doubled, the outgoing flux at the TOA reduces from 240 W/m^2 to 236.3 W/m^2 and the atmosphere absorbs and additional 3.7 W/m^2 of surface radiative power that was previously passing directly out the TOA the same as if the atmosphere wasn’t even there.

Busy? bored? Missed the clue that indicates that RW has never understood the basics of radiative transfer.

Review the first two responses from Myhre.

RW claims: “I find it very troubling and quite frustrating that something as basic and fundamental as this has apparently multiple intepretations all throughout the climate science community, and that I apparently can’t get a straight and definitive answer on the exact physical meaning of the RT calculated 3.7 W/m^2 per CO2 doubling.”

Actually everyone in the field has the same exact definition and it is written out in plain technical English in the IPCC report.

I know you can measure the absorption increase via RT simulation from that which is radiated from various layers of the atmosphere, but the question is does the 3.7 W/m^2 include reduction in emission to space from that which is radiated from the atmosphere itself? Or is it just that which is reduced from that radiated from the surface to space?

The 3.7 Wm-2 for a doubling of CO2 concentration is the net change in the absorption at tropopause level. The tropopause level is more relevant for surface temperature changes than change in the fluxes at the surface. I do not have values for the surface, sorry.

Cheers,
Gunnar”

Where does Myhre say where the newly absorbed power originates from? He doesn’t. I fail to see how this initial explanation of his contradicts where he confirms my final description of the origin of the absorbed power as being correct (i.e. that radiated from the surface which is absorbed through the whole atmosphere).

My interpretation is that Myhre blew you off by giving you the answer you clearly wanted to hear. What you fail to understand is that the forcing should be looked at more as a reduction in emission rather than an increase in absorption because absorption increases much less than emission decreases.

I do not have values for the surface, sorry.

If he doesn’t have the values for the surface, how can he possibly confirm that the reduction in emission is solely due to increased absorption of surface radiation?

The atmospheric profile tables should be obvious. You have the level number, the altitude in km, pressure in mbar and temperature in K for each level. Then you have the various components, mostly in atm cm / km. To convert to ppmv, you have to correct back to 1013 mbar and 273.2 K. For example, CO2 at the surface for the tropical atmosphere is 34.1 atm cm/km at a temperature of 299.7 K and a pressure of 1013 mbar. P1*V1/T1 = P2*V2/T2. So P1 = P2 and for unit area V2 = 10E5 cm we have V1 = 10E5*273.2*1013/(299.7*1013)= 0.9116E5. The volumetric mixing ratio is then 34.1/0.91158E5 = 374 ppmv. The table probably truncates rather than rounds because the value to two decimal places should be 34.18 atm cm /km. At 1 km V1 = 10E5*273.2*904/(293.7*1013) = 83011. 31.1/83011 = 374.6.

The next part has to do with slant paths through the atmosphere which isn’t being used so can be ignored. After that we get the cumulative absorber amount for the path length. At 100 km looking down, you get 302 atm cm total CO2 for a mixing ratio of 375 ppmv.

So now we come to the meat, the radiance vs frequency tables from 100-1500 cm-1. Column 1 is the frequency in cm-1. Column 2 is the wavelength in micrometers. Column 3 is the thermal emission from the atmosphere path in W/cm2/steradian/cm-1, column 4 is emission in units of W/cm2/steradian/micrometer. Columns 5 and 6 are the transmitted emission from the surface in the same units as columns 3 and 4. Columns 7 and 8 are reflected surface emission. I can’t find any conditions where these columns are not zero. Columns 9 and 10 are the total emission at the frequency/wavelength. Column 9 is the sum of column 3 and 5 and column 10 is the sum of 4 and 6. Column 11 is the integrated emission from 100 to xxxx frequency of column 9 and column 12 is the fraction of surface radiation transmitted to the specified altitude.

Note that the radiance units are not the same as in the graph. The graph is in W/m²/cm-1. To convert from the table to the graph, multiply by π steradians times 10,000 cm²/m²

When calculating the change in absorption of surface radiation, the average transmittance is not the correct value to use. You need to integrate the surface transmitted radiance from 100-1500 cm-1. The other thing is that zero km looking down is actually 1 m.

The worst case for a change in absorption is sub-arctic winter. For 9 km looking down, the reduction in emission for going from 375 to 750 ppm is 1.821 W/m². The increase in surface emission absorption is 1.400 W/m².

Factor of 2 error in the integration. The reduction in emission for sub-arctic winter is 1.8 W/m², but the increase in absorption is 2.74 W/m². For the tropical atmosphere, which is a substantial fraction of the Earth’s surface, it’s a reduction in emission at the tropopause of 4.58 W/m² while the increase in absorption is only 1.44 W/m²

I’ve looked at sub-arctic summer and mid-latitude summer and winter too. Mid-latitude winter also shows a larger increase in absorption than a decrease in emission while the others are the opposite. So emission and absorption aren’t directly coupled. This reminds me of Miskolczi. The ratio isn’t a constant and it’s unlikely to even average to a value of one for the planet.

I appreciate the responses everyone. Hopefully Myhre will respond and perhaps we can resolve at least this one thing.

In the meantime, I would like to try to explain/illustrate why a net absorption increase, whether all surface radiative power newly absorbed or not, should NOT be considered to be equal to that of post albedo solar forcing in its ability to act to warm the system and ultimately the surface, in particular.

For starters, the atmosphere effectively serves as the intermediating body between the surface and space, where the overwhelming majority of energy in the system is stored below the surface:

This means the atmsophere is primarly acting as a radiative flux filter between the surface and space, where absorbed radiative power (or energy moved into the atmosphere non-radiatively) is fairly quickly re-radiated, finding its ways either radiated out to space or to the surface somehow in some form. Also, all of the energy that enters the atmosphere has the potential leave the atmosphere over twice the area it arrives from. That is, in from the top (Sun) or bottom (surface) but then potentially out the top (TOA) or bottom (surface).

Put in the simplest way possible. Effectively, energy only flows in and out of the surface one way, but energy can flow out of the atmosphere two ways:

surface space

In addition to being the only significant source of energy, post albedo solar power is all downward radiated in and continuously acting to warm:

surface <–Sun
atmosphere <–Sun

Where as, radiated power flowing upward that is newly absorbed, when re-radiated (either via 'spotaneous' or 'stimulated' emission) always has a 50/50 probability of going up or down. When any of the newly absorbed energy is re-radiated up, it is in the act of cooling not warming (i.e. the flow of the energy is away from the surface towards space). Moreover, any time the newly absorbed energy is re-radiated back up it has the potential to pass into space, where as post albedo solar power never has this potential, because its continuously downward radiated in.

Basically, the reason is because not all the increased energy from absorption that warms the atmosphere will ultimately flow to the surface. It has equal potential to end up flowing away from the surface out into space.

Basically, the reason is because not all the increased energy from absorption that warms the atmosphere will ultimately flow to the surface. It has equal potential to end up flowing away from the surface out into space.

No, it doesn’t. You are still stuck on the half up half downand re-radiation mechanism thing. You couldn’t be more wrong. Atmospheric and surface temperature must increase by the same amount, assuming no change in lapse rate, to reduce the TOA forcing to zero whether the source of the forcing is decreased emission, increased incoming energy or some combination of both. Radiative forcing and radiative imbalance are exactly the same thing. Emission is only indirectly coupled to absorption by the temperature. There is no significant stimulated emission in the atmosphere, it’s all spontaneous. And please don’t say that spontaneous emission can’t happen because the time constant is too long. You’d just be embarrassing yourself even more, if that’s still possible.

I think you’re overlooking that because the atmosphere contains only an infinitesimal fraction of the energy stored in the system, it makes for a fundamentally different dynamic where the atmosphere is essentially a fast acting radiative flux filter between the surface and space. The energy that is flowing into the surface to sustain the surface temperature is mostly that of direct radiative power from the atmosphere and Sun and not by way of conduction (i.e. via collisions and diffusion).

The energy that is supplied to the surface to sustain the surface temperature is mostly that of direct radiative power from the atmosphere and Sun and not by way of conduction (i.e. via collisions and diffusion).

The GHE is primarily that of a radiatively induced effect, is it not? The primary mechnism is that of radiation flowing upward acting to cool that is absorbed and re-radiated back downwards, is it not?

The primary mechnism is that of radiation flowing upward acting to cool that is absorbed and re-radiated back downwards, is it not?

No.

It’s all about energy balance. The atmosphere is only partly transparent to LW IR but very transparent to incoming SW solar radiation and the temperature and density decrease with altitude in the troposphere which is 80+% of the atmosphere. Emissivity equals absorptivity so for any given surface temperature, the top of the atmosphere will emit less energy than the surface because it’s colder than the surface at the effective emission altitude and hence the surface at steady state must be warmer than it would be if there were no atmosphere. If it were the other way around, like it is in the stratosphere, the temperature would increase with altitude and the surface would be colder than it would be if there were no atmosphere.

When there is an imbalance at the top of the atmosphere, energy will accumulate or be lost from the system, changing the temperature in a direction to force the system closer to radiative balance. At steady state there will be energy balance at the TOA and the surface, but the details of the balance at the surface, unlike the TOA, depend on more than just emission and absorption of radiation. It also depends on vertical and horizontal movement of energy by air and water movement, including phase changes like evaporation and condensation of water, also known as sensible and latent heat transfer.

Your problem seems to be that you think, consciously or unconsciously, that you can track individual flows of energy in the system and that changes in those individual flows do not affect each other. It’s exactly the same problem you had with the KT97 and TFK09 energy balance diagrams. Changing the radiative balance by increasing CO2 does not create an independent energy flow that can go anywhere regardless of the physical properties of the atmosphere, i.e. “half up, half down”. Energy accumulates in the system as a whole, raising the temperature of both the surface and the atmosphere, which increases radiation at the top of the atmosphere, reducing the imbalance. If we keep the lapse rate, cloud cover and specific humidity constant, that increase in surface temperature and at every altitude in the troposphere will be ~1.1K. Almost exactly the same thing would happen if the total absorbed solar radiation increased by the same amount at constant CO2. That increase wouldn’t be a separate flow of energy either. It would be a change in the total flow.

Because RW has never studied the subject he is uniquely positioned to critique the work of the last 100 years of the field of heat transfer.

Not understanding the derivation of the radiative transfer equations, or the detail of the solution that is worked out from these equations allows RW to point out all the flaws in basic physics that we – and all those professors of physics – are blind to.

Look forward to the rewrite of Richard M. Goody’s seminal work “Atmospheric Radiation: Theoretical Basis”. Probably there will be a few less equations and a bit more hand-waving but that can only be a good thing.

Subrahmanyan Chandrasekhar will (posthumously) hand back his Nobel prize as the field of radiative transfer is rewritten without all that maths and physics.

I could go on.. but I need to get back to the article I keep trying to finish – Clouds & Water Vapor – Part Five – Back of the envelope calcs from Pierrehumbert

“The greenhouse effect is a process by which thermal radiation from a planetary surface is absorbed by atmospheric greenhouse gases, and is re-radiated in all directions. Since part of this re-radiation is back towards the surface and the lower atmosphere, it results in an elevation of the average surface temperature above what it would be in the absence of the gases.”

The fundamental mechanism of the GHE is that of radiative resistance to cooling (i.e. radiation flowing upward acting to cool that is absorbed and subsequently re-radiated back downwards). This is not the same thing as saying that the surface energy balance and surface temperature is soley determined by radiative effects. It certainly is not.

Now there’s a definitive source. Give me a break. Wikipedia has it’s uses, but it’s not a primary reference.

IPCC TAR Glossary:

Greenhouse effect
Greenhouse gases effectively absorb infrared radiation, emitted by the Earth’s surface, by the atmosphere itself due to the same gases, and by clouds. Atmospheric radiation is emitted to all sides, including downward to the Earth’s surface. Thus greenhouse gases trap heat within the surface-troposphere system. This is called the natural greenhouse effect.
Atmospheric radiation is strongly coupled to the temperature of the level at which it is emitted. In the troposphere the temperature generally decreases with height. Effectively, infrared radiation emitted to space originates from an altitude with a temperature of, on average, -19°C, in balance with the net incoming solar radiation, whereas the Earth’s surface is kept at a much higher temperature of, on average, +14°C.An increase in the concentration of greenhouse gases leads to an increased infrared opacity of the atmosphere, and therefore to an effective radiation into space from a higher altitude at a lower temperature. This causes a radiative forcing, an imbalance that can only be compensated for by an increase of the temperature of the surface-troposphere system. This is the enhanced greenhouse effect.[my emphasis]

I don’t see anything I’m saying as conflicting with any established physics. I’m genuinely puzzled why you keep insisting on this over and over.

This issue here is solely whether or not +3.7 W/m^2 of GHG absorption is equal to +3.7 W/m^2 post albedo solar power in its ability to act to warm the system and ultimately the surface in particular, since the energy flow into the surface is what determines the surface temperature. The ‘alculation of so-called ‘zero-feedback’ is not really a heat transfer calculation in the traditional, sophisticated sense, is it?

Can I ask:

Do you agree that +3.7 W/m^2 of post albedo solar power results in a so-called ‘zero-feedback’ warming of about 1.1C? (I agree with this, BTW)

Do you also agree that post albedo solar power is all downward radiated?

Do you also agree that +3.7 W/m^2 of GHG absorption always has a 50/50 probability of being radiated up or down in the atmosphere?

Do you agree that radiation emitted up in the atmosphere is in the act of cooling and not warming? (*In particular, the flow of the energy is away from the surface towards space)

Do you agree that all the radiation that passes into space from the atmosphere can only come from that which is radiated up and not down?

On a another issue, what do you think the probability of ‘stimulated’ emission from GHG molecules is in the atmosphere? Do you have any data or articles on that? Can you at least agree that if the probability of ‘stimulated’ emission is fairly high, the split of much of the newly absorbed energy half up and half down will occur virtually instantaneously? And multiple times over and over again for subsequent absorption and emissions?

Stimulated emission is extremely weak in all practical situations except lasers that are constructed with great care to make it strong.

The share of stimulated emission is determined by the strength of the electromagnetic fields that oscillate with the right frequency. The electromagnetic fields are very weak even in the strongest radiation as long as the radiation is not coherent. The coherence is obtained in laser cavity by the carefully tuned mirrors that keep the radiation that is directed along the axis of the laser inside the laser so long that the field strengths grow.

It’s perfectly safe to forget all effects related to the stimulated radiation in case of atmospheric IR.

I don’t have any issue with the IPCC’s definition of the GHE. I don’t see it as conflicting with the one posted a wikipedia at all. It’s just goes into more detail. I most certainly agree increased GHG absorption raises the average radiating altitude to effectively cooler levels, reducing the outgoing LW flux at the TOA, which in turn requires the atmosphere and ultimately the surface to warm in order to re-establish equilibrium with space. This seems basic and trival relative to what we are discussing.

Do you also agree that +3.7 W/m^2 of GHG absorption always has a 50/50 probability of being radiated up or down in the atmosphere?

No. Nobody but George White agrees with you on this and you are both wrong.

You cannot isolate the radiative forcing from all the other energy flows and treat it differently. There is no such thing as your concept of re-radiation. Instantaneously, the probability of being radiated up is zero because the emission upward has been reduced by that amount. At steady state, it’s 100% because the temperature has increased enough to increase emission upward and restore radiative balance.

So you do NOT agree the probability of all photon emission in the atmosphere, regardless of where in the atmosphere the emission occurs, is 50/50 up or down? You’re the first person I think I’ve encountered that has actually disputed this.

So you do NOT agree the probability of all photon emission in the atmosphere, regardless of where in the atmosphere the emission occurs, is 50/50 up or down?

Twist words much? Where did I say anything about individual photons?

The micro scale of individual photon emission and the macro scale of energy fluxes in W/m² are different things entirely. At the individual molecular level, for example, the Second Law doesn’t apply. Energy transfer is not limited to one way transfer from molecules with higher energy to molecules with lower energy. An individual molecule doesn’t have a temperature, it only has an energy which is distributed over all possible degrees of freedom, 3 kinetic and two rotational, plus a small fraction of two vibrational degrees (in plane and out of plane) and even smaller fractions of the two stretch vibrations (symmetric and asymmetric) when averaged over a large number of molecules. Any single molecule can have all its energy in any one of those degrees of freedom. (Describing quantum behavior in plain language is never completely correct).

The same sort of thing applies to emission. Just because the direction of emission of a photon by a single excited molecule is random does not mean that when there is a flux imbalance or forcing at the top of the atmosphere, half of that imbalance will immediately escape to space and half will be absorbed by the surface. At time zero after doubling, 3.7 W/m² of incoming solar radiation will not be radiated to space. It will be absorbed by the surface and atmosphere, raising their temperatures. The details of that absorption are complicated and require either a lot of assumptions or a full-bore GCM that actually works. As the temperatures increase, emission at the TOA will increase until steady state is reached again. At which point there will be energy balance at the surface and all levels of the atmosphere. There is no half up, half down. That assumption is incorrect for the system as a whole. It’s true at the micro level, but then we’re not talking W/m² anymore, we’re talking small fractions of an electron volt (0.0827 eV for 15 μm radiation) or some other equally small unit of energy.

Myhre told you in his first answer that you should concentrate on the TOA balance. But you still want detailed tracking of partial flows of energy. It doesn’t work that way. There are no partial flows except in your mind.

SoD has written a lot about radiation, that it exists and how, and this has been very informative, but, I still miss the complete comprehensible picture, of back radiation and how this can be responsible for the increase in temperature at the surface. Many details are debated in this thread, so I will reduce a lot, and try to take a look at the complete picture.

I have used some time pondering about how radiation is delayed and builds up as a feedback process between layers . And (I am not a physicist) starting with (mental) metal sheets, I have reached the same conclusion that Pekka describes on December 12, 2012 at 12:49 pm. But he also says that it’s not a god model for the atmosphere. Still, this is the model of the atmosphere as many layers, slabs, that shall be responsible for what is called the greenhouse effect, and is the main argument as such. (Taylor: Elemantary Climate Physics, p. 98) And if the first principal incoming radiation to the surface is let’s say about 65W, it’s not difficult to establish 390W at the surface and 65W out at TOA by means of a model of layers. In this case it would give five layers if they were absorbing all the radiation from one to the other both ways, (5+1)*65=390, more like the metal sheets. And even if this is far from sufficient for a detailed description for a turbulent atmosphere, it should do for a total consideration of the energy involved. With several competing processes the picture is of course more complex, but this is the main argument for the greenhouse effect. Does it always work like this, or is it just more or less, or maybe sometimes not at all?.

These arguments say that the greenhouse gases increase the temperature at the surface as a buildup through a feedback process of radiation between layers. As a model it is convincing. Further I presume it is based upon arguments of average values when it comes to 390W and the 15C. But it still have to prove it’s case for the more special occasions.

If the earth had no atmosphere we would expect the surface to be about 120C with a zenith sun (1365W/m^2). Not even a tropical desert with a very dry atmosphere and clear sky is near to that. Of course, not all the radiation will reach the ground, so in that case the atmosphere has a cooling effect. But even 1100W (a considerably reduction) would give 100C. If there was a very clear greenhouse effect as described above I would expect the energy to be increased by multiples and the temperature according to that. It does not seem to happen, on the contrary, the temperature in a case like this is even lower. So obviously the greenhouse effect seems here not to be at work at all. Why?

If the earth had no atmosphere we would expect the surface to be about 120C with a zenith sun (1365W/m^2).

And if the surface had zero heat capacity it would be -270 C when the sun went below the horizon. But with a heat capacity and rotation rate more like the actual Earth, the max temperature won’t be that high and the min temperature won’t be that low. As a result, the global average would be, assuming the same albedo, about -20 C.

You can compare this situation with a zenith sun on the moon, which will give this temperature on a surface that absorbs and reradiates. Se Wikipedia on The Moon about max surface temperatures. The rotation of the earth is not so fast that it should not work the same way if you use an absorbing surface with very little heat capacity. Do you think it would reach more than 100 C? Let’s even half the incoming radiation down to 680W, it should still result in 120 C by a modest doubling due to the greenhouse effect. By a multiple of six as I mentioned above it would be severe.

My argument is that the greenhouse effect under certain conditions also has to show its relevance both immediately and locally. I don’t think you address that situation I describe properly.

On Earth a hot surface is cooled by convection. In order to reach the temperature that corresponds to the level of radiation you must construct an vacuum enclosure with a window that lets trough all SW and LW radiation.

This is a plot of the temperature at the equator of a rotating sphere with and emissivity/absorptivity of 1 with a rotation period of 24 hours with rotational axis perpendicular to orbital plane with zero and non-zero heat capacity and TSI = 1368 W/m². As I remember, the heat capacity is about equivalent to the land surface of the Earth. If a deep water surface heat capacity were to be used, max-min would be less than 1 degree. Increasing heat capacity raises the average temperature while decreasing the temperature range. A superconducting surface sphere with an emissivity/absorptivity of 1 in orbit around our sun with an orbital radius of 1 AU would have a surface temperature of 5.4 C.

Parts of the lunar surface get as high as 123 C during the day, but also gets down to -153 C at night. It gets so cold that the energy received from the Earth makes the minimum temperature of the lunar surface facing the Earth about 20 K warmer than the opposite side.

The maximum daytime temperature with the sun directly overhead is only a small part of the global average temperature because it only occurs over a small area. Absent horizontal heat transfer, the poles will be still be extremely cold with intermediate temperature in between. I have the latitudinal temperature plot somewhere if you’re interested.

The model that’s based on metal sheets describes how radiative heat transfer proceeds. It tells that the heat transfer is made weaker and weaker by increasing the number of layers. In other words it gets weaker when an emitted photon is absorbed closer to the point of emission. This approach might describe the flow of energy in atmosphere if we would have only radiative heat transfer.

I present here another overly simplified and unrealistic description of the atmosphere. In this simplification the radiative heat transfer is made extremely weak by an atmosphere that very opaque for long wave radiation.

We continue to assume that solar shortwave radiation can penetrate the atmosphere and the surface is heated by that.

The assumption is that longwave radiation is very inefficient in transferring energy. Thus the surface is heated by radiation and would keep on warming without other mechanisms of heat transfer, i.e. convection and latent heat transfer (evaporation of water) (conduction is also taken as very weak as it is for real atmosphere). For simplicity I use the word convection for all that. Thermodynamics tells that convection will get so strong that the the atmosphere will reach a temperature profile determined by adiabatic lapse rate. As long as the temperature drops more rapidly with altitude the convection will get stronger, and it settles at the level were adiabatic lapse rate is observed.

In the stationary situation the surface is continuously heated by solar radiation and cooled by convection. Thus convection transfers all the energy received from sun up to the top of troposphere, where convection stops (troposphere is by definition that part of atmosphere where convection is present in the above way). Now we get all that energy to the top and must get rid of it. Here we must assume that radiation is not any more weak in transferring energy from TOA to space due to less dense atmosphere.

This second simplified case tells why the atmosphere has the adiabatic lapse rate through the whole troposphere. It’s seen that the same lapse rate is observed with a small energy flux and and a large energy flux. It’s the same always when convection is needed to transfer energy from lower altitudes. (Again some simplifications, but basically true.)

In this example the outgoing radiation has the strength of black body radiation at the temperature of top of troposphere, but the net radiative heat transfer at surface is very small. The IR radiation from the atmosphere to the surface is equal to the radiation from surface.

In real atmosphere we have some IR radiative heat transfer in troposphere but not enough the transfer all solar heating from the surface unless the temperature gradient is very steep, so steep that that temperature falls faster with altitude than adiabatic lapse rate. Under these conditions convection starts again and brings the lapse rate to adiabatic level. That happens whether the radiative heat transfer is very weak or only a little weaker than needed to stay below adiabatic lapse rate.

Now we have the situation of my second simplification but with the addition that radiation can transfer a part of the energy up from surface to top of troposphere. Net radiative heat transfer helps in getting energy from the surface to atmosphere and radiation that leaves the Earth may be emitted at any altitude from surface to TOA. All altitudes contribute to the outgoing radiation but high altitudes contribute more relative to the mass of air at those altitudes, because there’s less atmosphere between the point of emission and the space to stop the photons.

In real atmosphere we have an intermediate situation of the two simplified examples. The radiation to space is from all altitudes and there’s net IR radiative energy transfer also at surface. The latter is much smaller than the former but still significant.

I of course agree that the energy transfer process involves both convection and latent heat transfer as well as radiation (but they are not parts of the 65 W in my example). And a temperature profile based upon just radiation would be quite different (and non linear) from the near linear adiabatic lapse rate. And it can even seem intuitive that the convection will change a radiative lapse rate in the direction of the adiabatic lapse rate by moving air upwards. Still I find it puzzling that it can happen so fast and work so effectively that it practically seem to eliminate a multiple green house effect based upon radiation between layers, where one under certain local conditions would expect to observe it effectively at work. I find it difficult to deny an effect from greenhouse gases but I wonder about the strength.

And to DeWitt Payne,

yes I agree that a sphere as you describe in orbit around the sun with an orbital radius of 1 AU would have a surface temperature of 5.4 C, but that would be the effective temperature, based upon the same way of calculating as the earths mean temperature of 255 K without greenhouse gases, but with no albedo you will get the same 5.4 C. My point here is that the greenhouse effect as such works locally, where the sun is shining, and I expect to observe a direct effect where and when I happens. I am not sure if I do.

“Stimulated emission is extremely weak in all practical situations except lasers that are constructed with great care to make it strong.

The share of stimulated emission is determined by the strength of the electromagnetic fields that oscillate with the right frequency. The electromagnetic fields are very weak even in the strongest radiation as long as the radiation is not coherent. The coherence is obtained in laser cavity by the carefully tuned mirrors that keep the radiation that is directed along the axis of the laser inside the laser so long that the field strengths grow.

It’s perfectly safe to forget all effects related to the stimulated radiation in case of atmospheric IR.”

If this is indeed true, then this should mean most of the radiation emitted should be that of broadband and not narrow band, right? Or not? What is the probability that a collisional ‘bump’ will cause a GHG molecule to emit a photon? Can we all least agree that regardless of the mechanism that causes a photon to be emitted, the probability is always 50/50 that it will go up or down?

Your conclusion is not true. The linewidth of a laser beam might be narrower than the linewidth of the corresponding line in spontaneous emission, but molecular emission lines are narrow for spontaneous radiation as well. They are actually very narrow in the thin atmosphere of upper stratosphere but even with the line broadening due to molecular collisions of the lower atmosphere the lines remain narrow.

To expand on Pekka’s reply: Solids and liquids emit and absorb broadband radiation because the energy levels are so close together, not because they don’t exist. Planck originally derived his black body radiation formula from the concept of many closely spaced individual oscillators or energy levels. At low pressure, the energy levels for molecules are farther apart than the line widths. See for example the transmission spectrum of CO2 in a 1m path length cell at 296k with a mixing ratio of 0.00038 and a total pressure of 1013.25 mbar.

The central peak is for the transition from the ground state to the first excited vibrational state with no change in the rotational energy level. The branches on either side are for an increase or decrase of one level in the rotational energy state as well as a transition to the first excited vibrational state. At 296 K, many rotational energy levels are occupied so there are lots of lines. Here’s a log plot of the individual line strengths just for the central peak from 660-674 cm-1:
They aren’t resolved in the spectrum above because of pressure broadening of the line width at 1013.25 mbar. They can be resolved at low total pressure with a high resolution FT_IR spectrophotometer.

The following is not really significant for this discussion but for accuracy.

In typical liquids and solids the molecules or individual atoms and also electrons in the conduction band of conductors interact so strongly with each other that there are not similarly well defined vibrational or rotational discrete energy levels as in gases. There are much broader maximums in absorptivity that correspond to certain types of transitions but even those cases are quite different from gases.

The broad absorption peak of liquid water 3.0 µm is an example of such transitions but it’s really a broad peak rather than due to sets of nearby energy levels. It’s broadened mainly by the variable interaction of the hydrogen atoms with the neighboring molecules (the hydrogen bonds).

At higher energies of X-rays the energy levels are better defined even in liquid and solids.

Maxwell-Boltzmann distribution is strictly true only for an ideal gas, not even for real gases although it’s usually an extremely good approximation for them. What is more generally correct is that the probability of each state is proportional to exp(-E/kT) This proportionality leads to the Maxwell-Boltzmann distribution for ideal gas.

The Planck distribution of blackbody radiation is fundamentally a result of the Quantum Mechanical description of photons (or electromagnetic radiation). it’s not dependent on the properties of the material that emits the radiation when considered as follows.

The original and best description of blackbody is an isothermal cavity with fully opaque walls. Blackbody radiation is what exists inside such an cavity. The spectrum of radiation inside such a cavity does not depend on the other properties of the walls than full opacity.

A open surface may emit closely the same spectrum but never exactly over the whole range of wavelengths.

It wouldn’t hurt to read the earlier chapters on the physics and thermodynamics of the atmosphere too. Two things, though, first, if you disagree with something in Caballero, the probability is vanishingly small that you are right and he is wrong and second, just because you don’t understand it doesn’t make it wrong.

And even an oven with a small hole isn’t a perfect blackbody because of the hole. There will be a net radiation loss from the hole if the oven is above ambient or net radiation entering the hole from outside if the oven is below ambient. The nice thing about a box with a hole is that the emissivity of the walls doesn’t matter much. The spectrum of the photon gas is dependent only on the temperature of the walls. But low emissivity walls means the hole has to be smaller relative to the wall area for the spectra observed through the hole to match.

Because RW has never studied the subject he is uniquely positioned to critique the work of the last 100 years of the field of heat transfer.

I know, but for some reason I keep thinking RW isn’t hopeless. Besides, I’m retired and have nothing but time. Well, that’s not true either,

I’m seriously behind on my TV watching. There are many gigabytes of video on my PVR. I haven’t finished the latest season of The Walking Dead and am way behind on Burn Notice and several other series. Then there’s video games. I still haven’t finished Assassins Creed Revelations and Assassins Creed III is already out. I haven’t even loaded Uncharted 2. I did finish the main story line of Batman: Arkham City, but not all the side quests or DLC. Speaking of Batman, I hated The Dark Knight Rises. Bane and Ra’s Al Ghul are so underwhelming. I’ve downloaded the new Wing Commander game but haven’t installed it. I used to have a flight stick for old Wing Commander games and I’m not sure how it will play on an X-Box 360 controller.

Let’s look at the first meter of the tropical atmosphere in MODTRAN. I didn’t realize I could do this until recently.

For 375 ppmv CO2 and all other conditions default, the first layer emits 109.204 W/m², half up and half down because the layer is thin enough to be considered isothermal. It absorbs 53.519 W/m² of radiation from the surface and 54.361 W/m² from downwelling radiation. The layer emits more than it absorbs by radiation, a deficit of 1.325 W/m² so the assumption would be that the balance is made up by transfer from the surface.

That’s an increase in emission of 3.888 W/m² and an increase in absorption of 3.837 W/m² causing the imbalance to increase by 0.051 W/m².

And that’s just the first meter. If you go to thicker layers, half up and half down won’t apply because the layers aren’t optically thin and isothermal. A 100m thick layer, for example, will be 0.6 K cooler at the top than the bottom. In spectral regions where the transmissivity is close to zero, the bottom of the layer will emit more radiation than the top. The tropopause for the tropical atmosphere is 95 K cooler than the surface. As I said for the atmosphere as a whole, there is no half up, half down.

The micro scale of individual photon emission and the macro scale of energy fluxes in W/m² are different things entirely.”

Yes, of course. I’ve never suggested or implied otherwise. In fact, on more than one occasion I have specifically said that the atmosphere directly radiates more power out the bottom to the surface than it does out the TOA to space. However, this is primarily due to the lapse rate (i.e. because the bottom is warmer than the top), and NOT because the individual layers of the atmosphere anisotropically radiate their energy downward.

All radiation is individual photons. If the probability of emission of all photons is 50/50 up or down throughout the whole atmosphere, it can be deduced that half of the newly absorbed energy always has a 50/50 probability of radiating up or down (regardless of how many times it’s subsequently absorbed and re-radiated as well). The same is the case for any other energy finding its way into the atmosphere. Of course there is no way to ‘track’ the newly absorbed energy and the specific photons it emits, but this is not necesary to deduce that half of the energy, when radiated, will be radiated back up in the same direction it was going pre-absorption.

This is the whole point and the fundamental basis behind what White is claiming when he says “Of this, the atmosphere radiates half of this up and half down”.

The key thing is when any of the newly absorbed energy is re-radiated up, it is in the act of cooling not warming (i.e. the flow of the energy is away from the surface towards space). Moreover, any time the newly absorbed energy is re-radiated back up it has the potential to pass into space, where as post albedo solar power never has this potential, because it’s continuously downward radiated in.

“Your problem seems to be that you think, consciously or unconsciously, that you can track individual flows of energy in the system and that changes in those individual flows do not affect each other.”

No, I do not think this (really I don’t). There is for sure no way to trace individual photon paths. The system is far too complex and chaotic to do this (i.e. with energy changing forms and so forth).

“It’s exactly the same problem you had with the KT97 and TFK09 energy balance diagrams.”

I really don’t have any major issues with the Trenberth energy diagrams. I think they give a somewhat incomplete picture of what is actually happening, which has led to a lot of confusion among many, but I don’t think they are grossly wrong or anything. I certainly don’t think there are any 1st or 2nd law violations in them, as many claim. I also understand that their purpose is not really to provide a model of how the GHE works, but rather to just show global average energy flows. For example, I fully understand that the 102 W/m^2 of ‘evapotranspiration and thermals’ depicted is the net non-radiative loss from the surface to the atmosphere.

“Energy accumulates in the system as a whole, raising the temperature of both the surface and the atmosphere, which increases radiation at the top of the atmosphere, reducing the imbalance. If we keep the lapse rate, cloud cover and specific humidity constant, that increase in surface temperature and at every altitude in the troposphere will be ~1.1K. Almost exactly the same thing would happen if the total absorbed solar radiation increased by the same amount at constant CO2. That increase wouldn’t be a separate flow of energy either. It would be a change in the total flow.”

This is claim – yes, but I still maintain the 1.1K ‘zero-feedback’ at the surface and the equivalency to post albedo solar power is arbitrary and does not have a genuine physical foundation. Mind you, I fully accept the basics that the initial imbalance will cause the atmosphere and eventually the surface to warm in order to re-estabish pure radiative balance with space.

Given this discussion has gone on now for long time with many digressions and gaps, I think it would be useful, especially to any newcomers or lurkers, to lay out the fundamental issue in contention, which is the following:

“According to HITRAN based simulations, the atmosphere captures 3.6 W/m² of additional power when the CO2 is increased from 280ppm to 560ppm. Of this, the atmosphere radiates half of this up and half down. When the 1.8 W/m² of forcing power directed down is treated the same as 1.8 W/m² of additional solar forcing…”

I’ve compiled a summary list of my understanding (at least) of what George is doing and trying to show in the above ‘Proof that only half of absorption affects the surface’ analysis. Maybe this will shed some light in regards to what I’ve been trying to illustrate and say. (*Please do read the summary fully and carefully before commenting on the so-called ‘proof’ analysis, as in my experience, most of it is almost always misunderstood upon a first reading):

1. The model depicted at the beginning of the paper on the upper right is not a model of the actual behavior that occurs in between the boundaries of the surface and TOA in the real Earth-atmosphere system (i.e. in particular, it is not attempting to say anything at all about the amount of downward LW radiation emitted from the atmosphere to the surface, which in the real system, is estimated to be around 300 W/m^2 or more). Moreover, the model is not attempting to say anything about why the surface and TOA boundary fluxes are what they are, or why the surface temperature is what it is (i.e. why the surface energy balance is what it is).

2. The model is primarily built to strip the atmosphere down to the net flow of energy in and out of the whole system once all the energy circulating within the boundaries is taken away or subtracted out of the picture. That is, the model is built to show that the net effect at the boundaries would be the same if the simplified depicted behavior was what was actually happening (i.e. the surface temperature and outgoing LW flux at the TOA would be the same).

(*The reason why it is valid to consider only EM radiation for this purpose is because, excluding an infinitesimal amount from geothermal, the entire energy supply to the system is all EM radiation, and EM radiation is all that can pass across the system’s boundary between the atmosphere and space; and because the surface is so close to a black body, it specifically radiates the same amount of energy it is ultimately supplied as a result of all the physical processes in the system – both radiative and non-radiative).

3. The model and accompanying analysis applies to system in the steady-state (i.e. in equilibrium), and the model’s boundary fluxes are specifically and directly taken from the measured or derived boundary fluxes of the real system, from an approximate steady-state condition (i.e. directly via satellite and/or via the Stefan-Boltzmann law).

4. The fundamental assumptions going into the analysis and model are the following:

-Since the surface is very near a perfect black body, it cannot be receiving a net energy flow in of more than about 385 W/m^2 if it is also directly radiating 385 W/m^2 as a result of its temperature (287K), and at the surface, a watt of incident radiative power from the atmosphere is about equal to a watt of incident non-radiative power from the atmosphere.

-All non-radiative power leaving the surface has to be in addition to the 385 W/m^2 directly radiated from the surface.

-All the energy in the atmosphere is either on a path where it will be radiated out to space or received by the surface in some form. That is, there has to be an equal amount of energy coming out of the atmosphere as is going in, and there are only two ways out – either to the surface or out into space.

-The post albedo incoming solar flux of 239 W/m^2 is the only significant source of energy entering the system, and the atmosphere cannot create any energy of its own – all it can do is re-direct the energy supplied from the Sun.

-At the TOA, only radiation enters and leaves (i.e. it’s all photons coming in and going out)

5. The phrase ‘affects the surface’ located in title of paper, means the equivalent amount of surface radiative power absorbed by the atmosphere that effectively returns or ultimately enters the surface boundary as part of the net flow of energy in that sustains the surface temperature. In the real system, this amount can manifest itself at the surface as combination of radiative and non-radiative power (and no doubt is some combination).

(*A better title might be ‘Proof that only half of absorption acts to warm the surface’, or ‘Proof that only half of absorption is equal to post albedo solar power in its ability to act to ultimately warm the surface’)

6. Fundamentally, the analysis is applying Conservation of Energy to the already known surface and TOA boundary fluxes once the direct surface to space transmittance (the ‘T’ value) is computed from RT simulation. George White is calculating a ‘T’ value of 0.241, which means about 93 W/m^2 of the 385 W/m^2 radiated from the surface passes directly into space without interacting with the atmosphere (i.e. the same as if the atmosphere wasn’t even there). As a result of this, in order to satisfy the COE constraint that the planet radiate the same amount of energy out as is coming in (239 W/m^2), the remaining 146 W/m^2 required to be leaving has to be originating from the atmosphere (i.e. emitted from the atmosphere) instead of the surface, and 146 W/m^2 is also the remaining amount of non system entering power incident on surface boundary to sustain the surface temperature of 287K (i.e. 385 W/m^2 – 239 W/m^2 = 146 W/m^2, where 239 W/m^2 is the ‘system entering power’ from the Sun).

7. The ultimate point of the analysis is to show that when COE is applied to the boundaries (in the steady-state), only about half of the surface radiative power absorbed by the atmosphere, in its ability to ultimately warm the surface, is equal to that of post albedo solar power all radiated down into the system (or equal to the ‘radiative forcing’ of post albedo solar power). In addition to the fundamental assumptions layed out above, this is primarily because any surface emitted photon absorbed by the atmosphere has a 50/50 probability of being re-emitted up or down, and the same is the case on each subsequent absorption and re-emission until each photon’s energy either passes into space or returns to the surface in some form; and for any photon emitted in the atmosphere, whose energy was initially moved from the surface into the atmosphere non-radiatively, also has a 50/50 probability of being emitted up or down and the same is the case on each subsequent absorption and re-emission until each such photon’s energy either passes into space or is received by the surface in some form (*so too is the case in either scenario if the absorption of a photon by a GHG molecule causes the immediate emission of another, i.e. via ‘stimulated’ emission).

8. The context of the div2 analysis is largely that of so-called ‘zero-feedback’, which assumes the complexity or average net behavior of the complexity of all the physics of the atmosphere will not change upon a change in the energy balance, like when CO2 is doubled. So in order to calculate so-called ‘zero-feedback’, using George’s model, one just needs to multiply the post albedo solar or equivalent forcing (in this case 2xCO2) by the post albedo gain of the system (385/239 = 1.61; 3.7 W/m^2 x 1.61 = 6.0 W/m^2 = 1.1C from a baseline of 287K). That is, +3.7 W/m^2 of post albedo solar power has a ‘zero-feedback’ warming of about 1.1C, and +3.7 W/m^2 of atmospheric absorbed surface radiation, such as that which occurs from 2xCO2, has a ‘zero-feedback’ warming of only about half or 0.55C (3.7 W/m^2*0.5 = 1.85 W/m^2; 1.85 W/m^2 x 1.61 = 3.0 W/m^2 = 0.55C).

Now, for the sake of fairness and objectivity, I will say that my understanding is based on the 3.7 W/m^2 being all that of surface radiative power newly absorbed. That is, the 3.7 W/m^2 being the decrease in George’s ‘T’ and the increase in his ‘A’, as this is the fundamental starting point he is working from in the analysis. I will also say, that if the 3.7 is not the increase in surface radiative power newly absorbed, then my understanding at least is not correct; however, I then still do not understand if the 3.7 W/m^2 includes reduction in emission from that which originates from the atmosphere as well, how this would be equal to post albedo solar power since it too upon re-radiation would have have radiated back up in the same direction it was going pre-absorption.

RW, if you can find a textbook with a different first law of thermodynamics please present it. Please don’t say “I understand the first law of thermodynamics” when you keep claiming something contrary to the first law.

All I mean is that at 287K, in the steady-state, the net power supplied to the surface cannot be more or less than about 385 W/m^2. That’s it. You’re actually disputing this?

Do you NOT agree that the energy balance at the surface is the sum of radiative flux and non-radiative flux, and that the sum cannot be more or less than about 385 W/m^2 to sustain 287K?

Maybe I’m not using proper languange when I say:

“-Since the surface is very near a perfect black body, it cannot be receiving a net energy flow in of more than about 385 W/m^2 if it is also directly radiating 385 W/m^2 as a result of its temperature (287K)”

By all means please inform me how to use the correct terminology to say what I mean.

Honestly, I don’t understand why you think there is some kind of 1st law violation of what you call ‘K’ (non-radiative flux from the surface) being equal to the zero in the steady-state for the equvilent model. The simplified model is only built to show the net effect at the boundaries would be the same if its depicted behavior was what was actually happening. A basic requirement of COE for energy balance (i.e. an equilibrium state) in the real system is that all the energy entering the atmosphere has to eventually come out, with there only being two ways out – either to the surface or out into space. Given in the steady-state, all non-radiative power leaving the surface has to be in addition that directly radiated from the surface, any amount of it that finds its way radiated out to space has to be exactly offset by surface radiative power absorbed by the atmosphere but not exiting to space (i.e. finding its way back to the surface somehow in some form). Otherwise, this constraint of COE is not satisfied. Thus, in the steady-state, the net effect at the boundaries is the same as if ‘K’ is equal to zero or if all of ‘K’ that leaves the surface, returns.

Maybe it’s not clear that George’s simplified equivalent model says absolutely nothing about how a change in ‘K’ initated by a change in ‘T’ and ‘A’ could then subsquently change ‘T’ and ‘A’ further, eventually leading to new equilibrium state greater or less than ‘zero-feedback’? Maybe this is what is being fundamentally misunderstood?

Is it clear also that the simplifed model says absolutely nothing about why the surface temperature and surface energy balance is what it is? Specifically, it’s not ‘Proof only half of absorption is why the surface temperature is what it is’.

“A further constraint of Conservation Of Energy is that the global net non radiative flux between the atmosphere and the surface must be zero in the steady state if the radiative flux is also zero. While radiative flux to and from the surface can be traded off against non radiative flux, it makes no difference to the overall radiative balance.”

Meaning, it makes no difference to the calculation of ‘F’, for the purposes of what it’s being calculating it for, because we are already in the steady-state. Whatever amount of ‘cross exchange’ there is between radiant power from the surface and non-radiant power from the surface, it has already manifested the steady-state surface and TOA boundary fluxes. Of course, the amount of ‘K’ that leaves the surface and doesn’t come back makes a huge difference to why the surface energy balance is what it is.

———RW————-
..Your convection/latent heat flux of 100 W/m^2 is a net zero flux at the surface, because 100 W/m^2 is leaving the surface and 100 W/m^2 is returned to surface. In other words, 100 W/m^2 is entering the atmosphere from the surface and 100 W/m^2 entering the surface from the atmosphere..
———end——————————

———-RW————–
..By Conservation of Energy. We have agreed that energy cannot be convected out to space at TOA, right? All the energy entering and leaving is radiative.

If energy is convected from the surface into the atmosphere and some of that energy ends up radiated out to space, the amount of energy returning to the surface by convection will be less, right? Because energy has to be conserved, this will reduce the energy at the surface, cooling the surface and reducing surface emitted by an equal and opposite amount less than the more that was radiated out at the TOA. The same is true in reverse.

Latent heat of water is no different. Whatever amount leaves the surface and does not return (i.e. ends up radiated to space), will have a cooling effect, which will reduce surface emitted by and equal and opposite amount less.

In the case of latent heat, virtually all of this is returned in the form of precipitation, weather, etc. If there is an imbalanced, it will be equally offset at the opposite end (either at the surface or the TOA).

..As best as I can tell, you have invented a new law of thermodynamics. I summarize it in 3 points.

1. For every body space is the ultimate boundary of the encompassing system.
2. Radiation can only leave and enter the ultimate boundary via radiation.
3. Therefore, convective heat flux from any body within the system must be zero.

Is this your hypothesis?

I agree with steps 1 & 2.

You have invented step 3 and it appears you think it is obvious. But it’s not true and this is why heat transfer textbooks are full of conduction and convection calculations.

The surface of the earth has a net convective loss to the atmosphere. This is returned via radiation.

We can measure the radiation imbalance. We can demonstrate the convective heat transfer from the surface…
————-end————–

..I mentioned several times in this thread that COE dictates that atmosphere cannot create any energy of its own. You dismissed this as something obvious and that you already knew, but it is apparent to me that you don’t understand the constraint COE puts on the system and the energy flows at the boundaries of the surface and the TOA..
————-end————–

The heat from the sun evaporates water into water vapor and convection carries this up into the atmosphere. This is a flow of energy from the surface into the atmosphere. (Positive from surface to atmosphere, and estimated at about 80 W/m2 – I provided the calculation)

When it returns in the form of rain, the value of energy returned to the surface will be ?
What is the sign of this number (Positive from surface to the atmosphere)?

RW didn’t know the answer:

..I can’t produce a value of C-down, but I know one exists and is of significance (i.e. it can’t be ignored), which is my point.

– or even apparently understand the point of the question.

1. The heat transfer via the cold rain landing on the hotter surface can never be of the same magnitude as the latent heat originally carried away (I provided the equation with just a ΔT needed) and those with a calculator can find this out for themselves.

2. The sign of the heat transfer is positive from the surface to the atmosphere. Cold rain landing on a warmer surface cools the warmer surface. It doesn’t heat it back up.

If it isn’t apparent, what George White is fundamentally trying to show with the simplified model is the 50/50 equivalent split is an emerging property of the system upon an equilibrium state. That is, the complexity of all the effects and their many complex interdependencies, both radiative and non-radiative, averages out upon and equilibruim state to the same net behavior depicted the simplied model. Once such an equilibrium state is is altered by a change in the energy balance, like from increased CO2 absorption, the simplified model says nothing about how all the the effects in the system will change, eventually finding a way to new equilibrium state (either greater or less than ‘zero-feedback’). Only that it would (or should) average out to about a 50/50 equivalent split also. The reason, isotropic emission on the photon by photon basis in the unique conditions of the Earth atmosphere relative to the surface.

I seems no one can grasp the concept of a black box equivalent model, or why it is valid to use one for this particular purpose.

Do you agree that a black body, in the steady-state, must be supplied with 385 W/m^2 to sustain 287K? Do you agree that the surface of the Earth nearly exactly a perfect black body? If so, then by what physics or logic is not correct to say that the net energy it must be supplied is 385 W/m^2?

Maybe I’m missing something obvious here, but I genuinely do not know what it is. I’m not being obtuse here either. I really don’t know.

I agree the surface receives more direct radiative power from the atmosphere Sun than it emits, but much of this direct radiative power is replacing non-radiative power leaving the surface but not coming back, making it net zero energy flux entering the surface.

At 288K, the surface radiates 390 W/m^2, but receives 168 of SW from the Sun and 324 W/m^2 of LW from the atmosphere; however, 102 W/m^2 of non-radiative power is leaving the surface at the same time but not coming back. 168 + 324 – 102 = 390 W/m^2 = net energy supplied to the surface. That is the sum of the fluxes is equal to 390 W/m^2. This is all I’m trying to say.

At 288K, the surface radiates 390 W/m^2, but receives 168 of SW from the Sun and 324 W/m^2 of LW from the atmosphere; however, 102 W/m^2 of non-radiative power is leaving the surface at the same time but not coming back. 168 + 324 – 102 = 390 W/m^2 = net energy supplied to the surface. That is the sum of the fluxes is equal to 390 W/m^2. This is all I’m trying to say.

What is depicted in the simplified equivalent model is only the flow of energy that is going:

Sun -> space -> atmosphere -> surface -> atmosphere -> space

That is, specifically that which is flowing in and out of the whole system.

There is also another flow occuring entering and leaving the surface, which going:

Surface -> atmosphere -> surface

Only the former flow of energy is that which is adding energy to the surface. The latter is effectively a closed loop circulating within the system and part of the total energy contained in the system, albeit only an infinitesimal fraction of that contained below the surface.

Would you agree that not all the energy entering and leaving the surface is part of former flow of energy (i.e. what which is flowing in and out of the whole system)? If not, why not?

If the surface is not radiating the same amount of energy it is also being supplied, then there would not be enough energy (i.e. power) to account for all the energy flows in and out of both boundaries in the steady-state simultaneously, but there is. There are no ‘gaps’ in the radiative power fluxes in the simplified model. Hence, why it is valid to consider only the radiative boundary fluxes for the energy flowing in and out of the whole system, for the equivalent model.

Remember, as George himself has emphasized, the ‘equivalent’ in equivalent model only means any one joule is equivalent to any other. Really nothing more. That is, in the real system the surface is supplied with a net of 385 W/m^2, 239 W/m^2 enters from the Sun, and 239 W/m^2 exits at the TOA – the same net behavior at the boundaries depicted in the simplified model.

It’s clear you don’t have a clue. But the problem is that you don’t know you don’t have a clue.

The energy balance at the TOA is simple: 341.3 W/m² in from the sun, 79 W/m² is reflected by clouds and not absorbed, 23 W/m² is reflected by the surface and 78 W/m² is absorbed by the atmosphere leaving 161 W/m² of solar radiation absorbed by the surface. 78 plus 161 = 239 W/m² of absorbed solar radiation. The atmosphere emits 169 W/m² upward from the various greenhouse gases, mainly water vapor and CO2, The cloud tops emit 30 W/m² upward and 40 W/m² is transmitted directly from the surface without being absorbed by the atmosphere. 169 + 30 + 40 = 239 W/m² out from the top of the atmosphere. If you don’t round to the nearest integer it’s actually 239.4 W/m² in and 238.5 W/m² out leaving a net forcing of 0.9 W/m².

At the surface you have 161 W/m² of solar radiation and 333 W/m² of downward radiation from greenhouse gases and clouds. 161 + 333 = 494 W/m² in. The surface radiates 396 W/m² and loses 17 W/m² by sensible heat transfer and 80 W/m² by latent heat transfer. 396 + 80 + 17 = 393 W/m². ~ 1 W/m² is absorbed by the surface. Your surface → atmosphere → surface path is rightly ignored because it nets to zero. But the surface loses energy (cools) by two paths, radiation and convection (latent plus sensible). This convection is not part of the closed loop. It is a one way transfer. It is energy lost by the surface that will be radiated to space from the TOA. And yes, Virginia, convective energy transfer can be converted to radiative emission because emission depends on the temperature and convection keeps the atmosphere warmer than it would be without it so it emits at a higher rate.

The energy flows also balance within the atmosphere. The atmosphere absorbs 78 W/m² of solar energy, 356 W/m² of LW radiation from the surface and 97 W/m² from convection from the surface 78 + 356 + 97 = 531 W/m². It emits 333 W/m² to the surface and 199 W/m² from ghg’s and cloud tops to space. 333 + 199 = 532 W/m². If we just look at net in and out at the surface, it’s 161 W/m² solar in and 97 + 63 = 160 W/m² out.

You have said you don’t have a problem with this, but you apparently haven’t internalized the information. Otherwise you would recognize GW’s fundamental error in stating that the surface receives only as much energy as it loses by radiation. It receives more energy than it radiates and loses energy by both radiation and convection. The convective energy loss is ONE WAY. It is not a closed loop.

If the surface is not radiating the same amount of energy it is also being supplied, then there would not be enough energy (i.e. power) to account for all the energy flows in and out of both boundaries in the steady-state simultaneously, but there is. There are no ‘gaps’ in the radiative power fluxes in the simplified model. Hence, why it is valid to consider only the radiative boundary fluxes for the energy flowing in and out of the whole system, for the equivalent model.

If you were serious about understanding this subject you would get a heat transfer textbook, go through a few worked examples and try to do some exercises yourself.

..It is the process I’m trying to explain here, though obviously unsuccessfully.

Yes I know what it is. Clearly you don’t.

Is heat transfer linear?

Hang on, why am I answering you? I have disappointed you by asking you to study a textbook. Only someone who has never studied a subject yet thinks they are the master of it could possibly be disappointed by such a request.

“The heat from the sun evaporates water into water vapor and convection carries this up into the atmosphere. This is a flow of energy from the surface into the atmosphere. (Positive from surface to atmosphere, and estimated at about 80 W/m2 – I provided the calculation)

When it returns in the form of rain, the value of energy returned to the surface will be ?
What is the sign of this number (Positive from surface to the atmosphere)?

RW didn’t know the answer:

..I can’t produce a value of C-down, but I know one exists and is of significance (i.e. it can’t be ignored), which is my point.

– or even apparently understand the point of the question.

1. The heat transfer via the cold rain landing on the hotter surface can never be of the same magnitude as the latent heat originally carried away (I provided the equation with just a ΔT needed) and those with a calculator can find this out for themselves.

2. The sign of the heat transfer is positive from the surface to the atmosphere. Cold rain landing on a warmer surface cools the warmer surface. It doesn’t heat it back up.”

No, I agree with what you’re saying here. Maybe I misintepreted the questions or where you were going (or something). How many times have I said I agree that there is net non-radiative loss from the surface to the atmosphere, which accelerates surface cooling (i.e. the speed at which energy from the surface can be ultimately be transported to space).

I fail to see how this relates to anything being discussed here, but then again, as I said, maybe I’m missing something.

I cannot resist making one more comment on GW’s paper and your description of it.

You must agree that what GW has written is extremely short and skips many details. He can reach significant conclusions in such a short text only by making his own strong assumptions.

At least as you interpret the paper the problems are in part related to the handling of the non-radiative energy flux from the surface to atmosphere. You allow it to do different things in different connections. Allowing it to do almost anything makes it more likely that mistakes in discussion of radiative energy balance remain unnoticed.

Your language is very confusing when you refer to the combination of solar heating of the surface, LWIR from atmosphere to surface and the non-radiative energy flux from the surface in expression

4. The fundamental assumptions going into the analysis and model are the following:

-Since the surface is very near a perfect black body, it cannot be receiving a net energy flow in of more than about 385 W/m^2

The above is really confusing and seems to have confused you, as the total radiation is so much more and as the other fluxes from the surface are the ones that adapt to the radiative balance whatever this balance is.

The next points in your 4. do not help in making the comment less confusing.

Then in your point 6. you start to describe GW’s calculations which he does not even try to support by arguments that would be specific enough. There are just some vague comments that are supposed to justify them. This is probably the point where the calculation goes astray, although the paper is too vague to be sure where the error actually enters.

You have accepted so many results of standard understanding that I cannot understand how you refer to the GW calculation that leads to 93 W/m^2 from the surface directly to space as valid. The next conclusion is, however, the one which lacks are justification both from you and from GW.

.. and 146 W/m^2 is also the remaining amount of non system entering power incident on surface boundary to sustain the surface temperature of 287K

You just state the above. How can you think that it could be true when you have admitted that the atmosphere radiates more down than up due to differing temperatures? Here you really and fundamentally contradict yourself. You have accepted that there’s no simple relationship between the energies that the whole atmosphere radiates up and down, but here you claim again that they must be equal. After all you wrote a while ago:

Yes, of course. I’ve never suggested or implied otherwise. In fact, on more than one occasion I have specifically said that the atmosphere directly radiates more power out the bottom to the surface than it does out the TOA to space.

This sentence is in explicit contradiction with your other comments. You cannot accept this view and still claim that it’s known that the amounts are bound to be equal for a very closely related case.

The textbooks go trough all arguments in order keeping them self-consistent. Jumping to conclusions based of short papers like that of GW fails when the paper is not built on the textbook knowledge.

“You must agree that what GW has written is extremely short and skips many details. He can reach significant conclusions in such a short text only by making his own strong assumptions.”

I do agree that GW could go into more detail as well as further clarify what he’s doing and why.

GW did post this at Joanne Nova, which may help:

“It might help if I clarify what I’m trying to show here and why the approximations I’ve made are valid, even if they deviate from the specific internal processes in play. My goal was to quantify the required behavior of the atmosphere based on the boundary conditions between the atmosphere and space and between the atmosphere and the surface. Keep in mind that the behavior I derived at the surface boundary was a consequence of the behavior between the atmosphere and space, which by definition, is purely radiative.

Consider a hypothetical planet whose atmosphere has about the same amount of trace gas GHG absorption as the Earth, the same amount of N2 and O2, but has no water and all of the planets thermal mass is below the surface. In this case, my equivalent view of the energy balance is much closer to the actual physical mechanisms maintaining the balance. Where the current system gets complicated is with the movement of energy throughout the thermal mass. When contained within the oceans or atmosphere (i.e Hadley cell circulations), it is properly ignored. When the movement is between the oceans and clouds, where clouds comprise part of the thermal mass, the tendency is to count that movement as part of the energy balance, when it should more properly be ignored like the other circulation currents.

My equivalent view of the Earth is just as valid at quantifying the behavior dictated by the boundary conditions, but less accurate relative to representing the low level physical mechanisms establishing the balance, specifically between the surface and the atmosphere, once water is added and part of the active thermal mass of the planet is moved into the atmosphere. It’s also very important to recognize my simplified model is an equivalent model whose behavior at the boundaries matches the required behavior. That is, if the Earth’s actual atmosphere was replaced with an equivalent atmosphere with my specified behavior, the surface temperature would be exactly the same.”

“At least as you interpret the paper the problems are in part related to the handling of the non-radiative energy flux from the surface to atmosphere. You allow it to do different things in different connections. Allowing it to do almost anything makes it more likely that mistakes in discussion of radiative energy balance remain unnoticed.”

I want to make it absolutely clear that fully know in the real system there is no pure radiative balance at the surface because the surface is convectively coupled to the atmosphere.

“Your language is very confusing when you refer to the combination of solar heating of the surface, LWIR from atmosphere to surface and the non-radiative energy flux from the surface in expression

The above is really confusing and seems to have confused you, as the total radiation is so much more and as the other fluxes from the surface are the ones that adapt to the radiative balance whatever this balance is.

The next points in your 4. do not help in making the comment less confusing.”

I’m sorry if I’m not using clear language. I noticed you didn’t comment on number 5 in the list. I thought I covered what you’re referring to there. That is, where it says “in the real system, this amount can manifest itself at the surface as any combination of radiative and non-radiative power (and no doubt is some combination).”

“Then in your point 6. you start to describe GW’s calculations which he does not even try to support by arguments that would be specific enough. There are just some vague comments that are supposed to justify them. This is probably the point where the calculation goes astray, although the paper is too vague to be sure where the error actually enters.

You have accepted so many results of standard understanding that I cannot understand how you refer to the GW calculation that leads to 93 W/m^2 from the surface directly to space as valid.”

You mean the 0.241 ‘T’ and how it yields 93 W/m^2 or how the 0.241 ‘T’ is arrived at by GW?

“The next conclusion is, however, the one which lacks are justification both from you and from GW.

.. and 146 W/m^2 is also the remaining amount of non system entering power incident on surface boundary to sustain the surface temperature of 287K

You just state the above. How can you think that it could be true when you have admitted that the atmosphere radiates more down than up due to differing temperatures?”

All I mean by this is 146 W/m^2 is the amount of additional power that is being supplied to the surface that is not entering the system from the Sun(i.e. the only significant energy source).

Have you perhaps noticed that the 146 W/m^2 precisely quantifies the difference between surface radiative flux and the outgoing radiative flux at the TOA? And that this difference is that which is said to account for the +32C surface temperature as a result of the GHE?

“Here you really and fundamentally contradict yourself. You have accepted that there’s no simple relationship between the energies that the whole atmosphere radiates up and down, but here you claim again that they must be equal. After all you wrote a while ago:

Yes, of course. I’ve never suggested or implied otherwise. In fact, on more than one occasion I have specifically said that the atmosphere directly radiates more power out the bottom to the surface than it does out the TOA to space.

This sentence is in explicit contradiction with your other comments. You cannot accept this view and still claim that it’s known that the amounts are bound to be equal for a very closely related case.”

I’m not sure I understand what you’re referring to here. I thought I covered this with no. 1 in the list. Let me ask:

Do you agree that not all of the direct radiative power emitted from the atmosphere to the surface is part of the energy flowing in and out of the whole system (i.e. that which is flowing Sun -> space -> atmosphere -> surface -> atmosphere -> space), and that some of it can be part of the energy that is circulating within the system (i.e. that which is flowing surface -> atmosphere -> surface)?

It’s not possible to comment your point 5 than to tell that I cannot find any content in it. It appears just a few sentences put between 4 and 5 without any meaning.

As long as you cannot make the details of your ideas more understandable you obviously fail to understand yourself where your logic fails. Most certainly no-one of us three who have been writing comments to you has been able to find any consistent logic in yours or GW’s text.

I propose that you start by defining clearly what are the energy fluxes that you consider and denote each of them by a letter. Continue then by writing as formulas all the relationships between them that you consider well justified by some principle. Finally check, what you can solve from these equations. Come then back to us and show the outcome (the definitions of the fluxes, the equations and the solution). Then we should be able to discuss on these issues more rationally.

You may guess what I predict about the outcome but don’t let that distract you if you believe in yourself.

Over the last few days, as at many times over the past two years, people have arrived on this blog to explain how radiation from the atmosphere can’t affect the surface temperature because of blah blah blah. Where blah blah blah sounds like it might be some kind of physics but is never accompanied by an equation.

This point is equally valid for your ideas. The language of physics is maths. If you can’t write down a set of equations for your ideas it is because your ideas are confused. When you do write down a set of equations your ideas can be critiqued.

You seem to think the ~1.l K Planck feedback is an arbitrary calculation. It’s not. At the TOA at steady state we have 239 W/m² in and 239 W/m² out. Using the S-B equation to calculate an equivalent temperature we get 254.8 K. Now we instantaneously double CO2 and the outward power drops to 235.3 W/m² for a Teff of 253.8 K, a drop of 1 K. Now you may object to the use of the S-B equation to calculate Teff when the radiation does not have a pure blackbody spectrum, but this is, in fact, standard practice. It’s how IR thermometers work. They convert a temperature difference across an insulator with known thermal resistance to heat flow and a coating and add that heat flow to the emission from the surface of the insulator, which has an emissivity nearly equal to 1, which is attached to an otherwise insulated metal block with a measured temperature. The result is used with the S-B equation to calculate the measured temperature.

And again: If the outward emission at the TOA is reduced by 3.7 W/m², that power isn’t radiated half up and half down. It isn’t radiated at all. It’s absorbed. The temperature of the atmosphere and the surface go up over time as a result until 239 W/m² is again radiated upward. The downward radiance at the surface will be then be increased more than 3.7 W/m².

Even more precisely, absorption does not change by 3.7 W/m^2, net radiation at TOA changes by that amount, but that change involves many changes in absorption and emission within atmosphere. Among the immediate changes is an increase in radiation from atmosphere to the surface. Thus less IR emitted by the atmosphere escapes to space but more goes to the surface.

The IPCC definition of radiative forcing is strictly about energy flux through a surface and defines forcing as the difference between energy flux going in and energy flux going out through that surface.

But that definition has obvious implied consequences. Conservation of energy requires that if the flux going in is greater than the flux going out, then energy will accumulate in the system. I don’t know how you would describe that accumulation other than absorption. There are only three possibilities for the interaction of EM radiation with matter, transmission, reflection and absorption. For incident solar radiation we can rule out transmission except for limb paths through the atmosphere which are an insignificant fraction of the total. We account for reflection as albedo. The rest, by definition, must be absorbed. If energy didn’t accumulate with a positive forcing, why would you worry about forcings at all?

Even more precisely, absorption does not change by 3.7 W/m^2, net radiation at TOA changes by that amount, but that change involves many changes in absorption and emission within atmosphere.[my emphasis]

Yes, it does. Total accumulation of energy by the Earth system, atmosphere, cryosphere, ocean, etc.will increase by exactly 3.7 W/m². Where else is it going to go? The details of how the absorbed energy is distributed are indeed complex and change over time.

The IPCC calls the flux imbalance a forcing for a reason. That reason is that an imbalance forces the climate to change. My saying that the forcing is exactly equivalent to absorbed energy is, in my opinion, not contrary in any way to the usage by the IPCC of the term forcing.

Now I’m sure you’ll want to say something like “but downward radiation increases at the surface when you double CO2.” So what. Radiative forcing is calculated at the tropopause after allowing the stratosphere to reach a new steady state because convection effectively stops at the tropopause so energy transfer is all by radiation. That means that a forcing caused by an increase in incident absorbed SW solar radiation is equivalent to a reduction by the same amount of outgoing LW radiation. There is no half up half down when calculating radiative forcing, there is only down minus up. There will be energy flux imbalances at every level below the tropopause after an instantaneous doubling of CO2, but those imbalances are not used to calculate radiative forcing because they vary by location and altitude. What happens later is determined by the changes over time of the temperature, density and humidity profiles of the troposphere and convective energy transfer from the surface to the atmosphere. At the new steady state, there will be no flux imbalances anywhere on average.

By the way, when calculating energy coming in to the surface, one doesn’t usually subtract energy going out. It’s 320 + 170 = 490 W/m² in and 390 + 100 = 490 W/m² out, not 490- 100 W/m² in and 390 W/m² out.

I didn’t want to say that you have wrong views on anything substantial. I have, however, noticed that the statement “absorption in atmosphere is increased by 3.7 W/m^2” is made often also by people who support main stream views although that’s not an accurate description of the changes.

The minor error (or inaccuracy) of that formulation is a little similar to the gross errors that RW makes. In arguing against misconceptions of the type he has it’s perhaps useful to be very careful in avoiding even such inaccuracies.

It was meant for RW actually. Of course it’s not absorption by the atmosphere alone. It’s the surface plus the atmosphere. The ocean is a pretty big heat sink. Any increase in radiative forcing indicated by a positive radiative imbalance (down minus up) at the TOA, though, means that all of the imbalance must be absorbed somewhere in the system. A continuing increase in ocean heat content is a good indicator of a positive imbalance.

I’m not sure on the extent of disagreement here. I have seen comments from both RW and DeWitt declaring disagreement without being able to see what the disagreement is about. In some cases my impression has been that the comments have been interpreted to imply claims that they don’t state explicitly and that the disagreements concern only these assumed implied claims.

The IPCC definition of radiative forcing is strictly about energy flux through a surface and defines forcing as the difference between energy flux going in and energy flux going out through that surface. The additional points tell what is the state of the system which creates those fluxes (tropospheric temperatures unchanged, stratosphere adjusted to new balance).

The surface could be anywhere above the troposphere because the stratosphere as adjusted already and has a zero rate of warming for the assumed state.

The word “absorption” should not be stated in connection of the definition as the definition is not dependent on that.

In the theoretical estimation of the radiative forcing absorption and emission need to be considered but not in the definition.

The disagreement isn’t really about the definition of forcing but about what happens next. RW and GW, as near as I can tell, insist that all of the net absorbed flux will be absorbed by and immediately re-radiated by the atmosphere with half going up and half going down. This leads GW to conclude that no-feedback warming will be only 0.6 K, not 1.2 K because only 1.8 or 1.85 W/m² will affect the surface. This, of course, is completely crackers.

I know that the most significant disagreement is not about the definition. GW and RW do present further more concrete results that contradict strongly well understood physics. My impression is, however, that some of RW’s comments related to the definition have been essentially correct but dismissed unnecessarily as wrong. I cannot say for sure because the formulation has not been so clear that I could be sure that my understanding of it is the same RW has in his mind.

I wrote my comment trying to tell something on which everyone of could agree and to formulate it so clearly that it would be possible to come back to that when disagreement appears in following steps.

I don’t have great hopes on getting anywhere. This argumentation is probably of little help to others and therefore not among the most useful on this site. Formulating the correct ideas more and more clearly is useful as is resolving common misconceptions, but arguing with one person about ideas probably not shared in the same form by anyone else is of little value (I don’t believe that GW and RW have identical ways of thinking).

“The disagreement isn’t really about the definition of forcing but about what happens next. RW and GW, as near as I can tell, insist that all of the net absorbed flux will be absorbed by and immediately re-radiated by the atmosphere with half going up and half going down. This leads GW to conclude that no-feedback warming will be only 0.6 K, not 1.2 K because only 1.8 or 1.85 W/m² will affect the surface.”

I would say this is close, but not entirely correct. There is no requirement that all or most of the newly absorbed power has to be ‘immediately’ re-radiated. Only that is likely to be re-radiated fairly quickly, and when re-emission occurs half will be radiated back up in the same direction it was going pre-absorption.

The key thing is the 50/50 equilvalent split depicted in the simplified model is not being assumed, but is is emerging from the measured or computed boundary fluxes taken from the real and much more complex system. That is, just because the atmosphere will initially re-radiate only half of the newly absorbed energy down, this does not necessarily mean only half of this energy is acting to ultimately warm the surface the same as additional solar forcing (i.e. the same as post albedo solar power). This is the purpose of doing the actual proof in the div2 analysis via the black box model, which is really just built to apply Conservation of Energy to the surface and TOA boundaries in the steady-state. That only half of the surface radiative power absorbed by the atmosphere is acting to warm the surface is only proven or demonstrated when the required value of ‘F’ that emerges is 0.5 (as opposed to a value greater than 0.5).

As I understand it, GW’s point about Venus is that the atmosphere of Venus has a far higher heat capacity and far more energy stored than on Earth (relative to that below the surface), which means radiated energy absorbed by the atmsophere on Venus would end up spending more time in the atmsophere as a result of collisions with the surrounding molecules, resulting in a value ‘F’ greater than 0.5. This is the reason why in any case, one has to actually do the proof via the black box model and calculate the required value of ‘F’ to see how much of the additional absorption is actually acting to warm the surface.

Actually, I think it’s highly probable that a large fraction of the newly absorbed energy would be re-absorbed and re-radiated multiple times before the energy either finds its way radiated to space or is received by the surface in some form. The heat capacity of air is infinitesimal, which should mean absorbed energy, if thermalized, won’t stay thermalized very long before its re-radiated.

The key thing to conceptualize is all throughout the atmosphere individual photons are being flung equally in all directions. This is the fundamental physical basis behind the claim in GW’s paper where he says: “From the physics of black bodies, the atmosphere should behave as an isotropic radiator with half of it’s emitted power going up and half down” (not that the atmosphere as a whole, or even broken into separate layers, is isothermal).

The point is that the 3.7 W/m^2 is a change in the energy balance of the whole Earth system. That’s 100% present in the change of OLR at TOA, not 50% of that but 100%. (There’s a small correction from change in albedo due to absorption of SW by CO2, all the rest is change in OLR.)

The related change at the surface is not half of the 3.7 W/m^2 and the change at the surface has the opposite sign from the point of view of the atmosphere. At the top atmosphere emits less to space, at the bottom it emits more to the surface. The emission from the surface does not change in the situation used to define forcing but the emission from the atmosphere to the surface does by some fraction of the 3.7 W/m^2. What the fraction is cannot be concluded by any simple formula but must be calculated by a comprehensive model of the atmosphere and radiative transfer.

The heat capacity of air is infinitesimal, which should mean absorbed energy, if thermalized, won’t stay thermalized very long before its re-radiated.

You know, you can look up this sort of thing and it depends on what you mean by very long. The heat capacity of the atmosphere isn’t infinitesimal. The mass of air above a square meter of the Earth’s surface is 10,000 kg. The heat capacity of air is ~1 kJ/kg/K. So a quick and dirty calculation of the heating rate of the atmosphere column is 3.7/1E7 = 3.7 E-7 K/sec or 0.032 K/day. It will really be much less than that because a significant fraction of the imbalance would be absorbed by the surface, particularly the ocean where the heat capacity is much larger. The specific heat capacity of water is only four times as large as that for air, but water has a much higher density so for the equivalent heat capacity of the atmosphere, you need a depth of water of about 2.5 m. And the air above the water will warm at approximately the same rate as the water.

This is the purpose of doing the actual proof in the div2 analysis via the black box model, which is really just built to apply Conservation of Energy to the surface and TOA boundaries in the steady-state. That only half of the surface radiative power absorbed by the atmosphere is acting to warm the surface is only proven or demonstrated when the required value of ‘F’ that emerges is 0.5 (as opposed to a value greater than 0.5).

A value of 0.5 is only possible if the atmosphere is isothermal. In which case, there is no greenhouse effect if it’s the same temperature as the surface. Alternatively you can get a value of 0.5 if the atmosphere is a thin, isothermal slab at a lower temperature than the surface and with an absorptivity for LW radiation that is higher than the absorptivity for SW radiation. Neither case applies to the Earth’s atmosphere.

I finally looked at the div2 article of GW when you kept on about F =0.5. As I stated, you only get half up and half down for a single slab, isothermal gray atmosphere. And that’s exactly what I found. That’s a toy model. Over much of the thermal wavelength band the atmosphere is effectively black with a transmissivity very close to zero. That means F cannot not be 0.5. F does not emerge from GW’s boundary conditions, it’s built into them by the choices he made And he gets those wrong too.

The actual atmosphere is not only not gray, not isothermal, it’s also not perfectly transparent to incident solar radiation. Clouds and water vapor absorb about 1/3 of the incident radiation. Clouds are opaque in the near IR, which amounts to about 50% of the energy of solar radiation and water vapor has significant absorption as well. That blows the calculation of downward emitted atmospheric radiation because the surface only absorbs 161 W/m² of solar radiation, so the atmosphere would have to emit 224 W/m² down, not 146 W/m². But then it would have to emit 224 W/m² up too. But then the TOA doesn’t balance unless atmospheric transmissivity is greatly reduced. F is also now equal to 0.605, not 0.5. And of course he completely ignores convection. Since there is only the same amount of energy supplied to the surface as is radiated, he can’t account for global average precipitation of 2.5-2.8 mm/day/m². So we need another 100 W/m² emitted downward for convective energy loss and suddenly we’re back to KT97 and TFK09 energy balance range and an F very close to 1. GW’s model does not agree with observations. That means it’s wrong. Period.

As an example calculation: For the clear sky tropical atmosphere from 100-1500 cm-1 at 375 ppmv CO2, the surface emits 417.3 W/m². of that, 356.7 W/m² is absorbed and 348.23 W/m² is emitted downward from the atmosphere. Ignoring the 2% of downward radiation that is reflected not absorbed if the emissivity = 0.98, F equals 0.978, not 0.5. That’s something that Miskolczi observed from his calculations as well, although he tried to prove that F is identically 1. It’s not.

We can measure by a variety of means, the emission from the atmosphere to the surface, and it’s way more than 146 W/m² everywhere on the planet. Even for sub-arctic winter conditions, DLR is 162.9 W/m². That’s worst case for a small fraction of the Earth’s surface. While working on the Miskolczi threads, I did the same calculation for the other MODTRAN atmospheres with clear and cloudy skies. F is always nearly equal to 1.

Of course you can always take the position that the data and radiative transfer programs are wrong, but that’s only going to endear you with the tin foil hat brigade. If you still think that somehow GW is right and the rest of us are wrong, we can’t help you and I doubt anyone but Arfur Bryant and his ilk will pay any attention to you. I certainly won’t.

The fundament point you and everyone seems to be missing is, in the steady-state, all power in excess of 390 W/m^2 incident on the surface has to be exactly offset by power in excess of 390 W/m^2 leaving the surface, and that the surface specifically emits 390W/m^2 of radiative power solely due to its temperature (and emissivity, which is really close to 1). Moreover, any non-radiative power leaving the surface has to be in excess of that directly radiated from the surface, otherwise the surface temperature would be higher, where as there is no such requirement for the proportions of radiative and non-radiative power incident on the surface.

This is also why the power which is incident on and leaving the surface which is only flowing surface -> atmosphere -> surface (i.e. circulating within the boundaries) is effectively a closed loop in the steady-state, and the amount of cross exchange between radiant power and non-radiant power from the surface has to equal a net of zero in the steady-state.

This is also why the power which is incident on and leaving the surface which is only flowing surface -> atmosphere -> surface (i.e. circulating within the boundaries) is effectively a closed loop in the steady-state, and the amount of cross exchange between radiant power and non-radiant power from the surface has to equal a net of zero in the steady-state.

We’re not talking about energy that leaves the surface by convection and returns somewhere else like the Hadley cell flow. The 80 W/m² of latent convective transfer (evaporation/condensation) and the 17 W/m² of sensible heat transfer in TFK09 refers to the flow of energy into the atmosphere that doesn’t return to the surface anywhere. It’s not part of a closed loop. It’s radiated to space. Why you can’t accept that is beyond me. But even without that, GW’s analysis is irrelevant. It’s limited to the case where the atmosphere is perfectly transparent to incident solar radiation. And, it’s a toy model that is only slightly analogous to a real atmosphere.

But apparently your beliefs on this subject are deeply held and not subject to change. You will only accept things that confirm what you already believe to be true. Further discussion is therefore pointless. I officially give up.

It’s late, and I don’t have time for a full reply. I would only say that in your example of an IR thermometer, the energy is transferred via conduction and not radiation. Can we agree that, by and large, the energy transfer from the atmosophere to the surface is NOT via conduction, but by radiation?

What! You point the thing at what you want to measure. You can be a long distance away although the area of the field of view increases with distance.

The surface of the detector gains or loses energy by radiation only. It’s behind a plastic Fresnel lens. That’s why IR thermometers are called non-contact. The rate of energy gained or lost is by conduction, but that’s irrelevant.

The IPCC calls the flux imbalance a forcing for a reason. That reason is that an imbalance forces the climate to change. Saying that the forcing is exactly equivalent to absorbed energy is, in my opinion, not contrary in any way to the usage by the IPCC of the term forcing.

It’s true that the forcing is equal to power absorbed in the Earths system as a whole, but then it must be made clear that absorption is considered from the point of view of energy balance of the system as a whole.

The absorption in the atmosphere can be considered in many different ways. In one approach the absorption in the atmosphere is part of that overall effect. In that case atmosphere absorbs less than 3.7 W/m^2, because part of the 3.7 W/m^2 is absorbed by the surface (including oceans).

Another approach looks at the amount of radiation from the surface that does not escape directly to space.

A third one calculates the difference between emission from the surface and OLR at TOA. (This interpretation is probably not as common.)

A forth one sums all absorption that occurs in atmosphere both for radiation emitted by the surface and within the atmosphere.

As there are so many ways to choose for absorption and as only the first one corresponds exactly to the definition on radiative forcing, I feel that it’s better be careful with discussing absorption.

Take a copper sphere with a heater inside connected to an external power supply that is effectively invisible to the sphere with a surface are of 1 m² in deep space. Coat the surface so the emissivity is effectively 1. The heating elements are distributed throughout the sphere so we can ignore temperature gradients. Turn the heater on with a power setting of 400 W and go away until the surface temperature isn’t changing any more.

Ignoring the CMB radiadiation, the sphere will have a temperature of 289.8 K. Now we turn the heater up to 404 W. Does the surface immediately radiate the additional 4 W? No. The sphere would have to warm by 0.736 K. The sphere weighs 2527.6 kg and copper has a heat capacity of 384 J/kg/K so 714360 J would need to be added to the sphere to warm it that much. Worse, as it is warming, some of the added energy will be radiated away so it will take a lot longer than 67.5 hours to reach a new steady state. So after the first second, emission will only increase by a very tiny fraction of a watt. The same applies to the Earth after a reduction of emission at the TOA of 3.7 W/m². Effectively only a very little of it will be radiated away for quite some time.

Late to the party, but couldn’t resist: a copper sphere of 1 m2 surface area weighing 2.5 tonnes? The formula for spherical volume has a 3 in the denominator. Substantively, wouldn’t surface conductivity be more relevant than heat capacity to the problem?

[“If you still think that somehow GW is right and the rest of us are wrong, we can’t help you and I doubt anyone but Arfur Bryant and his ilk will pay any attention to you. I certainly won’t.”]

DWP, please don’t include my name in a separate discussion with RW. it is pejorative and unnecessary. You are perfectly entitled to carry on an esoteric discussion with SoD, Pekka and RW on whatever model calculations you wish. You are all perfectly entitled to draw whichever conclusions you wish, based on your beliefs.

I am only interested in the real world. I am interested in SoD giving an answer to my original question:

[“What do you think is the contribution made by CO2 to the ‘Greenhouse Effect’?”]

That question was followed by this statement:

[“I have a problem making sense of some of the high-percentage answers given by certain papers (eg Lacis, K&T), and would welcome the opportunity to hear your views.”]

I hope you agree that the question and statement were both polite and clear.

I am further interested in an explanation as to why, if the radiative theory is as accurate as you seem to assume, the ‘significant’ increases in nGHGs since 1850 have failed to produce a significant increase in temperature. No amount of handwaving and appealing to the authority of the IPCC on your part will take the place of a simple answer to a simple question.

So you can stop with the cheap shots by using my name disparagingly in a separate conversation. (My ilk…?)

I will continue to attempt pursue a respectful tone in any discussion in the face of persistent displays of sanctimony from those who wish to avoid brining reality into the debate.

At the top of the atmosphere in vacuum, energy can only be exchanged in and out by electromagnetic radiation. At the surface of the planet, that constraint no longer holds. The surface can exchange energy with the atmosphere by both radiation, conduction (sensible heat transfer) and the evaporation to vapor and condensation to liquid of water (latent heat transfer). Because air moves, the conductive boundary layer can be thinned resulting in a much higher temperature gradient and thus higher rate of heat transfer than if the air were stationary since conductive heat transfer is proportional to the change in temperature with distance (gradient). The combination of these is called convection because the energy is transferred by the physical movement of air. In Physical Meteorology, horizontal transfer can be referred to as advection and convection is then limited to vertical transfer. As far as I know, there is no scientifically established principle that convective heat transfer has to net to zero averaged over the surface of the Earth. If anyone can provide a reference to a paper published in a reputable, peer-reviewed scientific journal or widely used college textbook that contradicts this, please post a citation.

“The main idea in my previous comment was to emphasize that the Planck black body distribution is based on properties of radiation, not on the properties of the emitting surfaces.
The properties of surfaces determine how much less the intensity of emission is for each wavelength”.

The Planck distribution does depend on one property of the emitting surface in that its formulation was based on emission from an opaque/solid surface, as you wrote on December 19 at 7.55PM. Such a surface, made up of contiguous oscillating molecules, is nowhere to be found in the gaseous state where the oscillating/radiating molecules are free-floating in a photon gas. I think you have already affirmed (December 17) that it is entirely reasonable to seek a justification in physics for applying a formulation derived from one state of nature to an entirely different one; and that reprising SoD (as DeWitt suggested I do) is unlikely to reveal it.

Given that energy transport in the climate system is predominantly by mass transfer – planetary rotation, ocean currents, atmospheric convection and advection – the focus on radiative transport seems misplaced, except in the emission to space of energy moved non-radiatively from the surface to high in the troposphere where CO2 is the dominant radiative agent. Surface energy lost by radiative transport is constrained by the relative temperatures of the surface and its surroundings, viz., the atmospheric boundary layer. That is, flux is proportional to Ts^4*[1 – (T/Ts)^4]. Since the temperature gradient in the surface layer is small, T/Ts approaches 1, (T/Ts)^4 approaches even closer to 1 and the surface energy lost by radiative transport approaches zero. This is supported by K&T 1997 which notes that the atmosphere may absorb more solar energy, implying that the surface would lose less energy by LW radiative transport, than shown in the global mean energy budget.

The main function of the CO2 trace gas, then, is to convert molecular kinetic energy arriving by mass transport from the surface to radiation energy at an altitude/pressure above which transmission is sufficient to balance net incoming solar energy. The conversion involves molecular collision between visiting non-radiative molecules and radiative resident ones. It also involves interaction between radiative molecules and the surrounding photon gas. The strength of the conversion process is determined by the mass of the trace molecules and the efficiency of the interaction.

Increasing the mass of the energy-converting agent can only enhance the necessary energy conversion. However, obversely, it would also reduce transmission to space at any pressure/altitude; or, in other words, would raise the altitude above which transmission of outgoing LW balances incoming solar. This leads me to speculate that the net effect of adding CO2 to the atmosphere probably tends towards zero.

Anticipating objections, I have not overlooked emission, the intensity of which decreases with altitude, and therefore more CO2 means less radiation to space and a warmer climate system including at the surface. Rather, I question applying S-B to a gaseous non-surface, an application for which it may not be suited. In the atmosphere, emission occurs from individual molecules floating freely in a photon gas throughout the volume of a parcel of atmosphere, not from a contiguous surface layer of molecules.

I formulated my statement for the case of surfaces because describing emission from gases is a bit more complex. What you write on that is mostly correct but has some problems.

Radiative energy transfer is far from negligible in the atmosphere but in lower troposphere convection and latent heat transfer are more important. With increasing altitude the share of radiative energy transfer grows until it reaches 100% at tropopause.

Molecular collisions are so frequent that there’s never any problem in transferring energy from kinetic energy of N2 and O2 to vibrations of CO2 molecules and other GHG’s and through that to emission of IR.

Your conclusion that all this would reduce the influence of additional CO2 is misplaced as this influence comes to a major part from the changes in emission and absorption in the upper troposphere, i.e. exactly there from where the radiation can rather easily escape to space.

“Molecular collisions are so frequent that there’s never any problem in transferring energy from kinetic energy of N2 and O2 to vibrations of CO2 molecules and other GHG’s and through that to emission of IR”.

This seems to imply a degree of redundancy in the quantity of CO2 in the atmosphere, raising the saturation question. Or are you saying that the redundancy applies only to the transfer of kinetic energy amongst molecules because of the greater frequency of collisions amongst them than of exchanges between the radiatively active ones and the surrounding photon gas?

The concept of photon gas it a bit strange. Photons are emitted at one point and absorbed at another. Sometimes photons scatter or are reflected by material but even this can be usually neglected in considering IR. Photon-photon interaction is so weak that it can be totally neglected except in detailed analysis of lasers. The concept of photon gas could be used in discussing absorption but I don’t think that such use is common.

The redundancy applies, indeed, to the molecular collisions and their power to maintain the share of vibrationally and rotationally excited GHG molecules at the level that corresponds to the local thermal equilibrium. The emission strength of a particular wavelength from a volume of gas is equal to the number of molecules in the related excited state times a constant that’s the inverse of the life time of the excited state in absence of all collisions. The number of molecules in each excited state is exp(-E/kT) times the number of molecules in the ground where E is the excitation energy of the state.

There are so many collisions that almost all excited states lose their excitation in collisions but there are at the same time so many new excitations from other collisions that the number of molecules in the excited state stays as stated in the previous paragraph. Only when the number of collisions gets so low that emission is nearly as common, starts this situation to change. That’s the case in upper stratosphere, not in troposphere or even the lower part of stratosphere.

It’s not the S-B equation that’s applied to emission from a gas except to calculate the mathematical construct known as the effective temperature, Teff. Teff doesn’t have much of a physical meaning in terms of actual temperature. Emission is calculated from the product of the absorptivity/emissivity at a given wavelength and the Planck Equation evaluated at that wavelength and temperature. Kirchoff’s Law makes absorptivity ( = 1- transmissivity in the absence of reflection) equal to emissivity when it applies, and it applies in the atmosphere until you get to an altitude where local thermodynamic equilibrium no longer applies. That’s around 100 km for CO2. It’s fairly easy to prove that thermal emission, as opposed to emission from a laser or a lightning bolt, cannot exceed the emission from a blackbody at any wavelength without violating the Second Law. It can be less, but not more.

A not so obvious consequence of this fact is that if you take a blackbody at temperature T and place a gas cell with perfectly transparent windows in front of it also at temperature T, you won’t be able to see a change in the spectrum of the blackbody regardless of what gas you use to fill the cell. That’s because at the same temperature, emission will equal absorption. Again, that’s emission equals absorption, not that there is no absorption like the advocates of Claes Johnson might have you believe.

It’s not just CO2 that emits radiation in the atmosphere. It’s mostly water vapor. But since the scale height of water vapor is 1/4 that of dry air, emission from water vapor comes from a much lower altitude than CO2 where it’s warmer. That’s why CO2 causes a big dip in the emission spectrum space. The effective emission altitude is the altitude where the optical density equals one. That’s a transmissivity of 1/e.

I think I see your point: while integrating the Planck function across all wavelengths, as S-B does, is fine for blackbodies for which absorptivity/emissivity is universally 1, it’s not in the real world where these coefficients are wavelength-dependent. In practice, however, an average value for them is estimated independently and applied to S-B?

Nevertheless, this merely shifts the question of suitability of application from S-B backwards to Planck. When Planck saved Rayleigh-Jeans from the ultraviolet catastrophe, he did so by summing across the spectrum by serial definte integrals not by using the indefinte integral. He didn’t change R-J’s model – a cavity contained by solid surfaces.

Second para: In a system (the blackbody and the gas cell of varying composition) in thermal equilibrium, why would one expect any variation in the spectrum of either body? Next question: what makes you so confident that the condition is not characterised as emissivity = absorptivity = 0? After all, nobody has ever seen Prevost’s theory of radiative exchanges in action. But wait….I believe I know what your answer would be: the indirect evidence provided by remote sensing IR instruments. Incidentally, I’m more lone ranger than groupie in this enterprise.

The specialist teachers certainly understand which formula applies to each situation and use an applicable one. They may sometimes fail in pointing out why that’s true for the particular application although it’s not more generally.

Planck’s law is the one that’s valid in all these cases. S-B law and Wien displacement law can be derived from it for black body radiation. Planck’s derivation of his formula was, however, ad hoc. He couldn’t explain why the derivation was valid, only that it worked. The explanation came only with quantum mechanical description of interaction of matter with electromagnetic radiation and most completely by the work of Feynman and others in the form of quantum field theory and its subfield of quantum electrodynamics about 50 years after Planck’s original formulation.

Planck’s derivation of the formula for blackbody radiation was not based on existing physical theories. The law was derived from assumptions that could not be justified at the time. The success was one of the observations that led later to a totally new theory, Quantum Mechanics. QM as formulated in 1920’s and 30’s had still problems in handling electromagnetic phenomena, and a further development of quantum electrodynamics was needed to resolve them. It took about 50 years to get this far. Whenever any fundamental discussion is in order it should be based on the present set of theories, not on what the great scientists of past centuries were able to find out at that time.

Planck’s law remains correct, his derivation is obsolete. The suddenly common references to Prevost are even less justified (I think it’s fair to say that Prevost was not mentioned often anywhere until some skeptics started to use his name to justify some of their erroneous ideas). They are presented as if the understanding he had more than 200 years ago would be somehow superior to what anyone can read from physics textbooks now.

It’s fortunate that the difficult theories of quantum electrodynamics lead to the simple result that the simple view based on emission and absorption of photons turns out to be very accurate for most conditions. There’s no need to calculate photon-photon interaction and even the scattering of photons by matter is not always important. In particular it is not important in considering radiative energy transfer by IR in gas similar to the Earth atmosphere. For the calculation of the emission rate and absorption rate in gas the molecules must be described using QM but the coupling to electromagnetic field can be done using the simplest possible formulation.

“(I think it’s fair to say that Prevost was not mentioned often anywhere until some skeptics started to use his name to justify some of their erroneous ideas). They are presented as if the understanding he had more than 200 years ago would be somehow superior to what anyone can read from physics textbooks now.”

I think that you have no evidence for this.

Most sceptics would much rather explain EM radiation as a one way Maxwell- Rayleigh – Jeans approach between a hotter and colder object.

Prevosts understanding underpins the two way radiative interaction that is now the orthodox view.

I think I see your point: while integrating the Planck function across all wavelengths, as S-B does, is fine for blackbodies for which absorptivity/emissivity is universally 1, it’s not in the real world where these coefficients are wavelength-dependent. In practice, however, an average value for them is estimated independently and applied to S-B?

A pyrgeometer or precision infrared radiometer is, in fact, an integrator that has equal response for the range of wavelengths that are passed by the covering dome. So the measured IR flux is the integral over all wavelengths from about 3 to 50 μm. PIR’s are calibrated using a blackbody source. One can also measure the emission spectrum and integrate the intensities over all wavelengths. That’s harder, though, because most IR spectrophotometers don’t go to frequencies that low.

That flux can then be converted to Teff using the S-B equation. One could say that a PIR measures Teff and converts that to a flux using the S-B equation, but that’s not quite true. It really does measure flux, but it’s the flux coming into or out of the detector at a known temperature. Since the emissivity and temperature of the detector is known, that flux can be converted to a total flux impinging on the detector and thus the temperature of the source if you assumed that the source was a blackbody. That would also be the temperature of an insulated blackbody exposed to nothing but the radiation being measured. A pyrgeometer doesn’t ‘know’ what the spectrum is. It only knows the total received flux. If you had a laser at 500 cm-1 aimed at the detector, it would measure the total flux from the laser. The spectrum of the flux doesn’t matter. It’s the integral over the wavelength range that is measured. It’s also the integral over all wavelengths to which the Earth’s surface responds because it integrates over all wavelengths too.

The Earth’s surface isn’t really gray either. Emissivity does vary slightly with wavelength, but a constant emissivity is still a good approximation. The emission spectrum of the lunar surface has been used to determine local geology by looking at the variation of emissivity with wavelength. But you can use a PIR to measure the total flux and calculate a Teff. For an energy balance, it’s the integrated fluxes that matter.

Radiative transfer programs like MODTRAN calculate a spectrum and then integrate it over a frequency range, 100-1500 cm-1 for MODTRAN, to calculate total flux. Fluxes measured with PIR’s agree with fluxes measured by integrating the IR spectrum. I don’t understand why you have a problem with this.

Here’s a toy model that’s a lot closer to the real atmosphere than a grey, isothermal slab: Have a slab that is transparent in a window in the thermal IR and opaque everywhere else. Then let the slab have a finite thermal conductivity. As a first approximation give the slab 30% reflectivity for SW radiation and 70% transmissivity. Also, allow some thermal conductivity from the surface to the slab. You won’t get up equal up and down for thermal emission from the slab because it will be colder at the top than at the bottom, like the real atmosphere. You could set up a spreadsheet for this fairly easily, I think. I’m betting you could adjust the parameters to make the fluxes look very much like the real atmosphere.

“We’re not talking about energy that leaves the surface by convection and returns somewhere else like the Hadley cell flow. The 80 W/m² of latent convective transfer (evaporation/condensation) and the 17 W/m² of sensible heat transfer in TFK09 refers to the flow of energy into the atmosphere that doesn’t return to the surface anywhere. It’s not part of a closed loop. It’s radiated to space. Why you can’t accept that is beyond me.”

What I meant by the amount of cross exchange being a net of zero was the amount of non-radiative power leaving the surface that finds its way radiated to space. I’m well aware (and have stated many times) that 80 W/m^2 of latent heat and 17 W/m^2 of sensible heat depicted by Trenberth is the net non-radiative loss from the surface to the atmosphere. The point is in the steady-state, all the energy entering the atmosphere must be conserved, which means all the energy radiated from the surface must find its way out of the atmosphere, and there are only two ways out – either to the surface or out into space. If it’s not radiated to space, it is back to the surface somehow, which must then exactly offset the amount of non-radiative power leaving the surface but not returned. The net effect is the same as if it’s a closed loop, otherwise this basic constraint of COE is not satisfied.

I’m sorry if I’m not being clear. Let me try to put it this way, using ’97 K&T:

If 102 W/m^2 of non-radiative flux from the surface finds its way radiated to space, as you claim, where is the 320 W/m^2 absorbed by atmosphere from the surface radiative flux going? There is 165 W/m^2 radiated from the atmosphere to space, right? If 97 W/m^2 of this is from non-radiative flux from the surface, there is only 63 W/m^2 left. The other input to the atmosphere is 67 W/m^2 of post albedo solar energy absorbed by the atmosphere. In the steady-state, each one of these inputs to the atmosphere must either find its way to radiated space or to the surface in some form. That is, unless you think the energy in the atmosphere is monotonically increasing (and I’m pretty sure you don’t think this).

Yes, the ’97 K&T numbers balance. That’s the whole point. No matter which way you account for them they net to zero, satisfying COE in the steady-state. All of the flows which enter the atmosphere must come out by either going to space or to the surface somehow. There is also nothing implicit that the 102 W/m^2 of non-radiative loss from the surface to the atmosphere all goes to space. Some of it could return to the surface as part of the 324 W/m^2 if LW IR from the atmosphere. For any amount going out the top (TOA) or bottom (surface) there must be an amount equal to it going out the opposite direction so all the depicted boundary fluxes are accounted for.

For example, if all of the 102 W/m^2 goes to space, then the remaining 63 W/m^2 required to be leaving at the TOA from the atmosphere could come from any combination of the 67 W/m^2 and 320 W/m^2 absorbed by the atmosphere. If 63 W/m^2 of the 67 W/m^2 goes to space, that leaves 4 W/m^2, and 4 W/m^2 + 320 W/m^2 equals exactly the remaining 324 W/m^2 required to be going to surface as LW. There is no combination you can come up with where it won’t net to zero if all the energy depicted are accounted for. Of course the system is far too complex and chaotic to do an accurate accounting, but none the less this basic constraint of COE must be satisfied in the steady-steate.

This is really all GW means when he says:

“A further constraint of Conservation Of Energy is that the global net non radiative flux between the atmosphere and the surface must be zero in the steady state if the radiative flux is also zero. While radiative flux to and from the surface can be traded off against non radiative flux, it makes no difference to the overall radiative balance.”

“A further constraint of Conservation Of Energy is that the global net non radiative flux between the atmosphere and the surface must be zero in the steady state if the radiative flux is also zero.[my emphasis]

In a word, Duh. But of course, it’s not. In the TFK09 balance the surface absorbs 333 W/m² LW IR and 161 W/m² SW solar radiation for a total of 494 W/m². But it only radiates 396 W/m².

So the numbers in GW’s ‘black box’ model bear little relation to reality. Btw, it’s not a black box. That phrase refers to some device whose internal workings are unknown to the operator of the device. GW’s model is a variation on the classic single slab gray atmosphere model that is in every atmospheric radiative transfer textbook. You can also find it on RealClimate: http://www.realclimate.org/index.php/archives/2007/04/learning-from-a-simple-model/

But all these places point out that this model is not a realistic model of the Earth’s actual atmosphere. It only illustrates the most basic feature of an atmosphere that absorbs and emits more in the LW than it does in the SW, that the surface will be warmer than it would be if the slab were perfectly transparent. You cannot use this model to determine the magnitude of or limits to the increase in surface temperature with increasing LW absorption or the ratio of atmosphere emitted down to surface emitted up like GW claims.

But you can use it to prove that Wood’s 1909 much quoted experiment was seriously flawed, as was pointed out in the same journal a few months later by Charles Greeley Abbot. Everybody who cites Wood’s experiment as proof that there is no atmospheric greenhouse is either unaware of or, much worse in terms of intellectual honesty, ignores this fact. A later paper by Wood that claimed to mathematically prove that his experiment was correct contained a serious error that invalidated the proof. That was also pointed out at the time.

At this point, I’m left to conclude that you either haven’t been paying attention or are deliberately being obtuse. Or I suppose maybe you genuinely don’t understand (or are not really interested in trying to understand).

“You cannot use this model to determine the magnitude of or limits to the increase in surface temperature with increasing LW absorption or the ratio of atmosphere emitted down to surface emitted up like GW claims.”

I know, but this isn’t what GW is claiming in the div2 analysis with the black box model. I’ve said myself that his ‘equivalent’ model cannot be used to predict the increase in the surface temperature from increased LW absorption – be it greater or less than ‘zero-feedback’. In fact, I think I’ve said this multiple times now in various ways.

The simplified ‘equivalent’ model is only trying to show that the 50/50 equivalent atmospheric split is an emerging property of the system upon an equilibrium state. It says nothing about the path the system would take from one equilibrium state to another, which of course would be enormously complex and non-linear (be it ultimately more or less and ‘zero-feedback’), but only that whatever new equilibrium state finally manifests, it would (or should) average out to about a 50/50 equivalent split as well. The reason is isotropic emission on photon by photon basis in the unique conditions of the Earth’s atmosphere system relative to the surface.

The fundamental error in GW’s div2-page is that he mentions that there’s also other energy transfer from surface to atmosphere but then draws energy balances based on IR separately and presents formulas that cannot be correct when we have in addition a net transfer of energy from surface to atmosphere.

I genuinely fail to see how there is any 1st law violation. In fact, exactly the opposite. The entire exercise of GW in div2 is precisely based on the constraints the 1st law puts in between the boundaries in the steady-state. That is, the 1st law is actually the fundamental starting point GW is working from.

I assume you agree that the tiny contribution of energy from geothermal can be ignored for the purposes of what we have been discussing? That for all practical purposes the entire energy supply to the system is all EM radiation, and EM radiation is all that can pass cross the boundary between the Earth-atmosphere system and space? That the surface as a near perfect black body at 287K, specifically radiates the net amount of power it is supplied as a result of all the physical process in the system – both radiative and non-radiative? That all the energy that enters the atmosphere must come, and there are only two ways out – either to the surface or out into space?

I can’t reconcile these things with your claim of a 1st law violation.

What happens to the about 100 W/m^2 that the atmosphere receives from the surface by convection and latent heat transfer. The only way it can get out from atmosphere is radiation. Excluding it is a violation of first law.

GW writes about their effect as contributing only to redistribution of energy in the Earth system. That’s true but redistributing in a way that energy in very large amount flows continuously to the atmosphere is a huge violation of First Law (unless the atmosphere is actually warming with an extremely high rate). The First Law must be followed by each of the parts of the Earth system, not only by the system as whole.

Above all, the system as a whole must follow the 1st law. This is what GW is claiming, and forms the fundamental basis behind what he’s doing. I assume you agree that, in the steady-state, in the real system, the surface temperature and surface radiative power effectively stays steady? So do the fluxes in and out the system from space stay steady? At least on a 24 hour averaged basis. This is all that’s being depicted in the simplified model.

The non-radiative energy flow from the surface to the atmosphere primarily accelerates surface cooling (the speed at which energy from the surface can be transported back out to space). Overall, the non-radiative processes don’t cause warming. Convection is process that moves energy non-radiatively from the surface to higher parts of the atmosphere, where when radiated, has a greater chance of passing through the remaining atmosphere into space; thus making the surface cooler than it would otherwise be. The non-radiative processes hugely affect why the surface temperature and surface energy balance is what it is. As stated initially, GW’s analysis is not attempting to say anything about why the surface energy balance is what it is. If fact, his starting poing is to take the existing surface temperature and the fluxes in and out of the system from space which all of the complex processes of the system have already manifested (both radiative and non-radiative).

The whole point is the complexity and chaos averages out upon an equilibrium state and the average net behavior that occurs in between the boundaries is easily computed from the 1st law. I regret that apparently no one here can grasp what GW is doing, as it is an extremely useful approach to be taking, and has some really big advantages over those being used in traditional climate and atmospheric science.

The GW description fails totally on the energy balance of the atmosphere. Thus it’s totally wrong.

The First Law is not true for the IR of the atmosphere, it’s true for the total of all energy fluxes of the atmosphere and that includes convection and latent heat transfer that always add energy to the atmosphere (warming/cooling of the atmosphere must also be included to get the full balance, but the related power is small).

” finally looked at the div2 article of GW when you kept on about F =0.5. As I stated, you only get half up and half down for a single slab, isothermal gray atmosphere. And that’s exactly what I found. That’s a toy model. Over much of the thermal wavelength band the atmosphere is effectively black with a transmissivity very close to zero. That means F cannot not be 0.5. F does not emerge from GW’s boundary conditions, it’s built into them by the choices he made And he gets those wrong too.

The actual atmosphere is not only not gray, not isothermal, it’s also not perfectly transparent to incident solar radiation. Clouds and water vapor absorb about 1/3 of the incident radiation. Clouds are opaque in the near IR, which amounts to about 50% of the energy of solar radiation and water vapor has significant absorption as well. That blows the calculation of downward emitted atmospheric radiation because the surface only absorbs 161 W/m² of solar radiation, so the atmosphere would have to emit 224 W/m² down, not 146 W/m². But then it would have to emit 224 W/m² up too. But then the TOA doesn’t balance unless atmospheric transmissivity is greatly reduced. F is also now equal to 0.605, not 0.5. And of course he completely ignores convection. Since there is only the same amount of energy supplied to the surface as is radiated, he can’t account for global average precipitation of 2.5-2.8 mm/day/m². So we need another 100 W/m² emitted downward for convective energy loss and suddenly we’re back to KT97 and TFK09 energy balance range and an F very close to 1. GW’s model does not agree with observations. That means it’s wrong. Period.

As an example calculation: For the clear sky tropical atmosphere from 100-1500 cm-1 at 375 ppmv CO2, the surface emits 417.3 W/m². of that, 356.7 W/m² is absorbed and 348.23 W/m² is emitted downward from the atmosphere. Ignoring the 2% of downward radiation that is reflected not absorbed if the emissivity = 0.98, F equals 0.978, not 0.5. That’s something that Miskolczi observed from his calculations as well, although he tried to prove that F is identically 1. It’s not.

We can measure by a variety of means, the emission from the atmosphere to the surface, and it’s way more than 146 W/m² everywhere on the planet. Even for sub-arctic winter conditions, DLR is 162.9 W/m². That’s worst case for a small fraction of the Earth’s surface. While working on the Miskolczi threads, I did the same calculation for the other MODTRAN atmospheres with clear and cloudy skies. F is always nearly equal to 1.

It appears you either didn’t read nos. 1 & 2 in my summary list, or you are unable to grasp the concept of a black box equivalent model, which does require some unconventional thinking (and is somewhat difficult). The simplified equivalent model is really only built to show that the net flow energy at the boundaries would be the same as that which occurs in the real and much more complex system. That’s pretty much it.

On Earth, in the steady-state, at a surface temperature of 287K, 239 W/m^2 post albedo solar power enters, 239 W/m^2 LW infrared exits at the TOA, and the surface is supplied with a net of 385 W/m^2 – the same as that depicted in the simplified model. Thus, the net flow of energy at the boundaries in the real system is the same as that depicted in the simplified model. That is, the same as if half of what’s absorbed by the atmosphere is radiated into space, never to be incident on the surface. Energy and power never received by the surface cannot warm the surface (or be acting to warm the surface). In the end, it’s literally this simple.

Maybe this is a classic case of mindset bias combined with it seeming too simplistic to be correct. Or maybe I’ve somehow missed something, which seems to be what everyone is insisting, but I’ve yet to see a clear line of evidence or logic demonstrating so.

Are we all in agreement that the calculation of so-called ‘zero-feedback’ means no changes in anything else anywhere, in particular, no changes non-radiative flux from the surface denoted by SoD as ‘K’? This includes not just at the surface, but any behavior in between the surface and the TOA – no matter how non-linear and complex?

The reason I mention this is because I think this is perhaps the crux of the disagreement, and why no. 8 in my summary list is critical.

“The redundancy applies, indeed, to the molecular collisions and their power to maintain the share of vibrationally and rotationally excited GHG molecules at the level that corresponds to the local thermal equilibrium. The emission strength of a particular wavelength from a volume of gas is equal to the number of molecules in the related excited state times a constant that’s the inverse of the life time of the excited state in absence of all collisions. The number of molecules in each excited state is exp(-E/kT) times the number of molecules in the ground where E is the excitation energy of the state”.

This derivation of radiative flux in a gas is to me more intuitively satisfying than that used in the simple models in which fluxes of equal (S-B) power densities issue in up and down directions from the upper and lower “surfaces” (itself a gross distortion) of a thin layer, respectively. A MODTRAN thin layer in the troposphere is one kilometer thick displaying a 6.5 degree C temperature gradient or, proportionately near the tropopause (220K), about 3%, implying a 12% flux difference between the two surfaces, the larger flux directed downwards. This is in direct contrast to the “more up than down” directional partition of EM energy generated by a free-floating molecule in a volume of atmosphere. Which derivation does MODTRAN follow?

Your understanding of radiative transfer calculations is way oversimplified.

MODTRAN, LBLRTM, SpectralCalc, etc. all use the same formulation, the optical density is calculated for the layer thickness at a series of frequencies. For MODTRAN, the frequencies are every 2 cm-1 from 100-1500 cm-1. MODTRAN uses a moderate resolution band model to calculate the optical density based on the number of molecules per unit area in the layer. A line-by-line program uses frequency resolution that is higher than the line widths and calculates optical density based on the hundreds of thousands of individual lines for each molecule using data from the HITRAN database. HITRAN includes factors to calculate Doppler and pressure broadening of the individual lines. For an l-b-l program, there may be contributions from many lines at each frequency and thousands of lines may need to be tested at each frequency to see if they make a significant contribution. The lines from isotopologues, like 16O13C18O, are different from each other and are tested and calculated separately. An l-b-l can produce megabytes of data for relatively narrow frequency ranges.

The optical density is converted to transmissivity by taking the exponential of the negative of the OD. Emission up is the sum of the transmissivity times the total emission from the layer below (emitted plus transmitted) plus one minus the transmissivity (absorptivity) times the value of the Planck Equation for the radiation frequency and the temperature of the layer, not the upper surface of the layer. Similarly, the emission down is the transmitted downward radiation from the layer above plus the emitted downward radiation. Radiation up and down emitted from the layer is equal.

The Stefan-Boltzmann equation isn’t used at all. The total emission is integrated over the calculated wavelength range from the point of view of an observer looking in a particular direction at a particular altitude, usually straight up or straight down.

The layers of MODTRAN are so thick that the temperature is significantly different at the bottom and top of each layer. The change of density is not either the same at the bottom and top. The optical thickness of each layer is large at 15 µm and other wavelengths of highest absorptivity.

This means that MODTRAN cannot represent in great detail the profiles. The errors that are made in the description of each layer are not totally negligible. It turns, however, out that a model of 34 layers can provide more accurate answers for larger scale questions than we might expect from the errors made in calculation of each layer. How can we know that? It’s simple, we can try with different number of layers and see what’s the lowest number of layers that gives accurate enough answers. That way we get a model that’s accurate enough and as fast as possible in practical applications using the basic methods of that model. The same argument is used in choosing, how broad the frequency bands should be.

To conclude: It’s important that the temperature profile and density profile are taken into account in calculation of radiative energy transfer, but it’s not necessary to go into further details than MODTRAN does.

It doesn’t matter whether you want to find the bending moment in a concrete beam, the heat transfer through the atmosphere, or the population of a predator in an ecosystem – the fundamental equation set ends up being differential equations.

Then when you want to solve a differential equation in real life with actual boundary conditions almost always you have to solve it numerically.

A numerical solution is always inexact. It doesn’t have infinitely thin layers, or widths or time slices. It has finite slices.

As Pekka says it is pretty easy to demonstrate that the numerical solution is a good approximation simply by increasing the number of layers, widths or time slices. That’s what is explained in numerous papers on this subject. As a useful example, Water Vapor Feedback in the Tropical Upper Troposphere: Model Results and Observations, Dessler & Minschwaner, Journal of Climate (2004):

..The model is maintained on a fixed-pressure grid, with 300 levels from the surface to approximately 30 km and a mean layer thickness of 100 m. This fine vertical resolution is necessary to capture small changes in the maximum height of convective detrainment and in vertical gradients of the subsidence mass flux in the UT.

They don’t attempt to teach calculus in their paper, just do what any competent scientist would do in assessing their own results..

I did it myself with my MATLAB model used in the Atmospheric Radiation and the “Greenhouse” Effect series that uses the complete HITRAN database of absorption lines. I played around with the Δv (linewidth “slice”) and Δp (pressure “slice”) for my numerical solution to see how sensitive the result was to these changes.

You have a number of distinct problems in your questions:

1. You question fundamental physics – radiative exchange between two bodies – this is well-established physics for well over 100 years and I am not interested in trying to prove basic physics that is accepted in every heat transfer textbook and used in every relevant heat transfer field – as stated in the Blog Etiquette under Basic Science is Accepted. Others might be interested, up to them.

2. You appear not to have actually understood anything written on this blog about radiative transfer. Therefore you stated that I teach that the Stefan-Boltzmann law is used for radiation from the atmosphere. This is not correct. You also state that notable climate scientists teach this. Also not correct. Well, I can’t be bothered to link you to 10 articles I have written that explain something different. If you want to claim something, please provide proof.

And as a note, see again the Blog Etiquette under “Attributing Ideas to People Incorrectly – and then not facing up to that when it is pointed out.”

And just for the record, for anyone else – the calculation of emission and absorption of radiation from the atmosphere does not use the Stefan-Boltzmann equation. When you find this equation used in introductory atmospheric physics textbooks it is to provide simple teaching examples. If only people read to the end of the textbook.. See, as an example, Simple Atmospheric Models – Part One.

Based on following your site closely for several months and occasionally for much longer it seems clear that basic questions are asked both by people who just don’t have the physics education needed to understand these issues already but who are fully willing to learn, and by people who are convinced that they have a better knowledge from own ideas or more commonly from all kind of wrong sources. Trying to convince the second group may be futile but a little more help could be given for the newcomers.

I haven’t gone through all your material but based on some attempts I have the feeling that a little more text on the physics fundamentals might be useful. Perhaps all that is already somewhere but certainly it’s not easy to find. Having a well organized set of physical basics would be helpful also in later discussions when a good reference can be used.

I understand that adding such material is a major effort. Much of that’s already available in different places on the net, part of that is covered rather well in Wikipedia, but having well organized material in your style would be helpful. Material like the lecture notes of Rodrigo Caballero are perfect for some but too much and too difficult for many. There may be good sources elsewhere but I don’t know about any that would complement properly your site. The Caballero lecture notes could be of great help in figuring out what to include and how to present that. For maximal benefit it would be necessary to link the material also to your other posts where the ideas are expanded and used in a proper context.

Based on following your site closely for several months and occasionally for much longer it seems clear that basic questions are asked both by people who just don’t have the physics education needed to understand these issues already but who are fully willing to learn, and by people who are convinced that they have a better knowledge from own ideas or more commonly from all kind of wrong sources. Trying to convince the second group may be futile but a little more help could be given for the newcomers..

First of all, I really appreciate your patient contribution on this blog.

Second, the first group of people you refer to are a major focus of this blog, and the second group, well, I’d like to try.

I’d appreciate any suggestions from you as to how to organize material.

When I first started the blog I spent time at many other climate blogs reading the comments on physics subjects and writing comments in response. Then I wrote articles that attempted to address the confusion that was demonstrated. Comments in response to these articles generated further articles that had “another go at it”.

Also I studied the areas I did not understand through textbooks and many many papers and wrote articles that addressed my own earlier areas of confusion. This is an ongoing work as there is much to understand.

The question of how to address the wide world out there is a tricky one.

It embraces everything from:

a) “insightful” people who have cheerfully driven a wrecking ball through 100+ years of physics because it matches their ideas about climate science

b) people who can’t write an equation and don’t even believe one is necessary if it contradicts their conceptual understanding

c) people who claim physics degrees but seem unwilling to make something like a simple calculation of entropy

d) people who often know much more than me and want to understand the basis of certainty or probability for much of the IPCC and climate science consensus on the impact of doubling CO2

Yes, it’s a big world.
Any ideas on improvement or categorization or article subjects will be gratefully received.

John Millet
I hope you have grasped that advice from De Witt, Pekka and SoD.

You need to master the format and solution of differential equations.
A degree course in Climate Science would do no harm.
Studying the user manual for MODTRAN is of course essential.

Then perhaps you can understand why the near surface temperature of the Earth has not risen for the last 16 years.

Pay no heed to sceptics like the Theoretical Physicists Gerhard Gerlich and Ralf D. Tscheuschner;
Falsification Of the atmospheric CO2 greenhouse effects within the frame Of Physics” by Gerhard Gerlich and Ralf D. Tscheuschner; International Journal of Modern Physics B, Vol. 23, No. 3 (2009)
Pages 48 to 50 of PDFhttp://arxiv.org/PS_cache/arxiv/pdf/0707/0707.1161v4.pdf

or the Astrophysicist Joseph Postma.
They say that the Radiative Transfer Equations derived correctly for Stars cannot be used for Planets.

If Postma is correct, how do you explain the fact that those supposedly incorrect equations produce calculated atmospheric emission spectra that agree very closely with measured spectra? Clear sky radiative transfer is considered a solved problem in physics. Much of the early work was done or supported by the US Air Force to use in the design of things like heat seeking missiles. Those work too.

As far as the temperature trend, if you cherry pick starting dates, you can produce about any trend you want in the last 10 to 20 years. The thirty year trend continues to be positive and hasn’t decreased significantly, which it would have if the temperature had been truly flat for the last 16 years.

Your continued belief that G&T are correct tells us more about you than it does about climate science.

If you only look for articles that agree with your point of view, you’ll never make any progress.

Continuing: My grasp of the math being somewhat tenuous, is my interpretation correct: Emission strength varies directly with the number of molecules in the excited state consistent with LTE; that number of molecules is a proportion of the number of molecules in the ground state; the proportionality decreasing with temperature? If so, increasing the mass of the radiatively-active molecules, which would increase the number of molecules in the ground state, would also increase the number in the excited state and, therefore, strength of emission (albeit, the relative rate of increase declining with temperature and altitude). This appears to be in direct contrast to the typical explanation: adding CO2 raises the altitude and therefore lowers the temperature and strength of emission, resulting in net warming of the climate system.

The effective altitude of emission for a given frequency is defined as the altitude where the optical density is equal to one calculated from the TOA downward. The optical density is proportional to the total number of molecules per unit area in the path. Increasing concentration increases the number of molecules at every altitude so the altitude where the OD equals one increases. Higher altitude equals lower emission because the temperature is lower for the same optical density.

The emissivity at a given wavelength varies with the number of absorbers (=emitters). The emission at a given wavelength is a function of the Planck equation x the emissivity.

You can think of it like this – the Planck equation essentially accounts for the proportion of molecules in each energy state.

This appears to be in direct contrast to the typical explanation: adding CO2 raises the altitude and therefore lowers the temperature and strength of emission, resulting in net warming of the climate system.

You are mixing up two separate ideas:
1. the basis of statistical thermodynamics which is at the molecular level
2. the macro level which uses the result of statistical thermodynamics along with atmospheric basics

That is, there is no contrast, or contradiction.

A colder atmosphere absorbs exactly as much as a warmer atmosphere. But a colder atmosphere emits less than a warmer atmosphere. If the atmosphere contains more absorbers then the solution to the radiative transfer equation is less emission. We can picture this as emission from a higher altitude, but in practice the atmosphere emits from every altitude.

I said “If the atmosphere contains more absorbers then the solution to the radiative transfer equation is less emission. We can picture this as emission from a higher altitude, but in practice the atmosphere emits from every altitude.”

The reason the solution to the radiative transfer equation is less emission is because the atmosphere gets colder the higher up we go. With more absorbers (more GHGs) any given slice of the atmosphere will be absorbing more and emitting more. The solution ends up being an average emission to space from a higher altitude, therefore a colder location, therefore lower emission.

The solution to the equation is pretty simple from a numerical point of view, although tedious due to the need to integrate across all wavelengths, then through all layers – but the solution matches the measurements from FT-IRs as I’ve demonstrated many times.

Do atmospheric layers at different temperatures absorb exactly the same amount of EM energy? Isn’t the amount of absorption a function of the mass of the absorber and isn’t this greater in warmer layers than in colder ones?

The strength of absorption is not influenced much by temperature, it’s determined by the properties of the molecule and the number of molecules in the volume passed through per unit area. There’s a weak temperature dependent effect from the reduction in the share of molecules in the vibrational ground state. That starts to affect significantly CO2 only at temperatures well above the highest atmospheric temperatures, because more than 90% of CO2 molecules are in their vibrational ground state for temperatures that occur anywhere in the atmosphere.

The mass of the absorber enters in the calculation of the number of molecules. Each type of molecule has also both a different mass and a different vibrational states. The excitation energies of these vibrational states are affected by the masses of atoms but also by their interactions. Having said all that I don’t think that there’s such dependence on mass that you seem to have in mind.

“Fluxes measured with PIR’s agree with fluxes measured by integrating the IR spectrum. I don’t understand why you have a problem with this”.

The second “measured” should read “calculated”. What is measured by the PIR is a minor portion (X, usually negative) of its recorded output (DLR) which is the sum of X and calculated S-B for surface temperature. Taking K&T 1997 figures: 324 = -66 + 390, that is, the PIR measures 20% of DLR, the rest is a theoretical calculation. A 1% error in the PIR’s recorded output is a 5% error in its measuring skill. Stoffel 2005 reported +/- 15Wm-2 pyrgeometer precision which on the above figures is over 20%. Pyrgeometer precision would be even worse (30%) on K&T’s numbers adjusted for suspected 18 Wm-2 more absorption of solar in the atmosphere, implying X = -48. Not the most compelling of evidence for radiative exchange, though the only type available.

That’s ± 15% for a single reading of a single instrument. There are lots of instruments out there making measurements 24/7. The average precision of all those readings is a lot lower than ± 15%. PIR’s are not the only instruments used to measure atmospheric IR emission either. FT-IR measured spectra agree within 1% or so with calculated spectra.

I misread, that’s 99% of all instruments are within ±15 W/m² for the total observed radiation. At 333 W/m², that’s less than ±5%. Your handwaving argument to make that measurement error appear to be worse than it is is without merit. If your logic were correct, then the error in the measurement when there is zero flux at the surface of the detector would be infinite. Approximately zero flux is the norm for a cloud covered sky, that is Teff of the sky is ≅ Tambient. Or do you think that PIR’s can somehow violate the Second Law. No flux in or out is the definition of having the same temperature.

Results of the FIRE II experiment’s BSRN-sponsored Infrared Radiometer Intercomparison at Coffeyville, Kansas suggest that the manufacturer-supplied calibrations for pyrgeometers are acceptable to within approximately 15 W/m2. However, before SURFRAD pyrgeometers go into the field, they are recalibrated at Table Mountain against standard instruments whose calibrations are traceable to the world standard in Davos, Switzerland. This is a novel technique developed at SRRB that appears to improve the absolute calibrations such that 90% of the measurements are within 11 W/m², and 99% are within 15 W/m² of the standards. At the Calibration Facility’s field site at Table Mountain near Boulder, Colorado, SRRB maintains three reference instruments of each type that the SURFRAD instruments are checked against before and after deployment.

Oh, and the measurement instrument specified for implementation of the International Temperature Scale for temperatures above 700 C is an optical pyrometer, specifically a disappearing filament optical pyrometer. Calibration of the temperature of the tungsten ribbon filament lamp vs current flow through the filament is described below.

This document describes the realization and dissemination of the International Temperature Scale of 1990 (US-90) above 700 “C at the National Institute of Standards and Technology (NIST). By using fundamental principles of blackbody physics, the US-90 scale is first fixed at the freezing point of gold (T90 = 1064.18 “C) and is then extended to temperatures between 700 “C and 2700 “C by determining the ratio of the spectral radiance of a tungsten ribbon filament lamp to that of a gold fixed-point blackbody at a wavelength of 655.3 nm.[my emphasis]

The lamp is placed in the field of view of the instrument and the current through the filament is adjusted until the ribbon disappears, i.e. has the same color as the object being measured. The temperature of the object can then be calculated from the temperature of the filament using the current vs. temperature calibration.

So please don’t keep trying to tell us that using the Planck Equation or it’s integrated form, the Stefan-Boltzmann equation, can’t be used to measure temperature and radiant flux. The sky may not be a black body, but the detector in a PIR is a good approximation of one.

“…that’s 99% of all instruments are within ±15 W/m² for the total observed radiation. At 333 W/m², that’s less than ±5%”.

It seems you are using the later global mean energy balance numbers than the 1997 ones I used.: 333 = -63 + 396. My point is that there is no measuring error in the 396 number because it is not a measurement, it is a calculation based on a theory. Therefore, observed instrumental precision must be instrumental measuring precision, in this case 15/63 or 24%. As mentioned earlier, taking account of a reduced measured portion of the PIR reading, as canvassed in K&T 1997, would magnify the error. No handwaving here.

True if you only make one measurement with one instrument. But that’s not the case. Make ten independent measurements and it’s ±1.6% u.s.w.

Speaking of grading lab experiments, give your lab supervisor Wood’s 1909 paper and see what he says. You would get a failing grade for poor documentation if you submitted anything like that in any undergraduate physical chemistry lab course. Most middle school science fair projects are better documented.

My point is that there is no measuring error in the 396 number because it is not a measurement, it is a calculation based on a theory.

Oh, please. So now you’re saying that you can’t use the S-B equation for a solid or liquid surface either? Calculations of interplanetary probe orbits are based on a theory too. And again, the error in the average is much less than the error in the measurement of an individual instrument. Besides, downward LW in TFK09 isn’t a measurement either, it’s the amount necessary to close the energy balance after all the other fluxes have been calculated from a variety of measurements. The point is that radiative transfer calculations are supported by measurements. PIR’s are one form of those measurements.

From TFK09:

Therefore, we have a lot more confidence in the values we have assigned than indicated by the spread within the tables. TOA values are known within about ±3% or better, except that the net is (or was) 0.85 ± 0.15 W m−2 (Hansen et al. 2005), and surface fluxes are constrained within 5% except for solar-reflected, LH, and LW, where errors may be as much as 10%.

.

LH being latent heat transfer. The errors are also constrained by the fact that the numbers have to add up so that energy in is approximately equal to energy out at the surface, within the atmosphere and at the TOA. Reduce downward LW while keeping upward surface emission constant and everything else has to change. Either you get less absorption of solar radiation in the atmosphere and more by the surface or convective heat transfer must decrease or some combination of changes of those fluxes. That’s because the global average temperature implied by the surface emission has to be in the ballpark of the actual global average temperature (or, more accurately, global temperature distribution). LH is constrained to be at least the energy transferred by the amount of water that evaporates to produce the average rainfall over the planet. The numbers are not simply pulled out of the air or somewhere else.

But even if there are errors as large as you claim, downward LW emission from the atmosphere still significantly exceeds upward LW emission at the TOA everywhere it’s been measured, which verifies the existence of an atmospheric greenhouse effect. Nor does it imply that the actual average numbers vary naturally over a wide range. Given known physics, an increase in ghg’s must result in some increase in surface temperature. There are only a few scientists with adequate qualifications who dispute this. What we can or should do about this is a completely separate question and beyond the scope of this blog. It is the Science of Doom, not the Politics of Doom after all.

“If your logic were correct, then the error in the measurement when there is zero flux at the surface of the detector would be infinite. Approximately zero flux is the norm for a cloud covered sky, that is Teff of the sky is approx Tambient”.

Observations from a population of pyrgeometers under clouded skies would not vary because all observations would comprise only the precise calculated component.

The top level equation GW gave me for the energy budget is Pi = Po + dE/dt, where Pi is the power incident on the system from the Sun and Po is the power emitted by and reflected by the planet, and dE/dt is the sensible heat. If tau = E/Po, GW says the equation can be re-written as Pi = E/tau + dE/dt.

I think it’s best to just quote GW directly for the rest (I don’t think he’ll mind), as it seems very advanced to me (maybe some of you can help me understand all of it):

Quoting GW directly:

“Po can be expressed in terms of surface and cloud temperatures, the fraction of the planet covered by clouds, surface and cloud reflectivity, atmospheric absorption from GHG’s and the fraction of absorbed power that leaves the planet.

Po = E/tau = p*(Pi*Rc + Pc*Fc) + (1-p)*(Pi*Rs + Ps*Fs)

where Rc and Rs are cloud and surface reflectivity, Pc and Ps are the power emitted by the clouds and surface, Fc and Fs are the net fraction of Pc and Ps that leaves the planet and p is the fraction of the surface covered by clouds. Note that atmospheric emissions are bundled into an effective Fc and Fs and is equal to some fraction of the surface and cloud power absorbed by GHG’s in the atmosphere.

where K is a constant dependent on the physical properties of the planets energy storage system.

The variables available from the ISCCP data set are, Rc, Rs, Ps (Ts), Pc (Tc), p, Pi and consequentially, Po, dE/dt and dT/dt. Given measured values and HITRAN based simulations of absorption, there are enough equations to independently solve for f and K, where f is the “equivalent” (added by me, RW) fraction of power absorbed by the atmosphere thats returned to the surface. The variable f relates Fc and Fs to the calculated absorption fractions As and Ac, where (1-Fx) = (1-Ax) + f*Ax.

This model forms the basis for what I’ve matched to satellite data. The div2 model has enough equations to solve for p*Fc + (1-p)*Fs (the average net transmittance) and is a simplified version of the above model with dE/dt set to zero.”

End quote.

Basically, as I understand it, the div2 simplified model is built to calculate the equivalent fraction of the surface radiative power absorbed by the atmosphere that must exit the planet on global average upon an equilibrium state (i.e. find its way radiated from the atmosphere to space). The idea is to show that when this is done the emerging value of ‘F’ required for energy balance, for the system as a whole, is equal to 0.5 (as opposed to a value greater than 0.5, or a value of 1, which would be required for GHG absorption to be equal to that of post albedo solar forcing).

GW’s calculations only apply to his toy model of a gray slab atmosphere, not the real world. The LW emission of a single slab toy model is not anywhere close to that for the real atmosphere. The real atmosphere, after all, emits more LW down than up, unlike the slab atmosphere which is constrained to emit equally up and down. And you always get a value of F = 0.5 for the slab atmosphere if the atmosphere is perfectly transparent to incoming SW radiation, which also isn’t true of the real atmosphere, presuming you solve it correctly. The emission from the atmosphere must be directly proportional to the absorptivity and the fourth power of the slab temperature. The slab temperature and the surface temperature are constrained by the incoming solar flux. Face it. It’s a toy model that says little about the real world. With a more accurate radiative transfer model like MODTRAN where the temperature and density of the atmosphere decrease with altitude, F is always very close to 1.

Yes, this is obvious and confirmed by actual measurements of downward LW at the surface. The same is true of a separate layer in the atmosphere with a temperature differential between the top and bottom of the layer, where the bottom is warmer than the top (i.e. the bottom of the layer will directly radiate more power out the bottom of the layer than is radiated out the top). All of this is basic and obvious. I can only conclude either you haven’t read my initial summary list (no. 1 in particular), or you just haven’t been paying attention.

A fundamental point here is SoD keeps saying that GW is assuming non-radiative flux from the surface, designated as ‘K’, is equal to zero in the steady-state, and that this is unjustified and requires proving it.

Here I will prove that setting ‘K’ to zero, as GW does in his boundary equations, must result in the same net flow of energy at the boundaries in the steady-state, and that this is all GW is claiming by setting ‘K’ to be equal to zero.

Using Trenberth’s ’97 numbers, which are steady-state, the surface at 288K radiates 390 W/m^2 into the atmsophere. Of which, 70 W/m^2 (or just 40 W/m^2 – it doesn’t really matter for this exercise) passes directly into space. 320 W/m^2 is therefore absorbed by the atmosphere. In addition, there is 102 W/m^2 of net non-radiative moved from the surface to the atmosphere, and 67 W/m^2 of post albedo solar power absorbed by the atmosphere. So 320 + 102 + 67 = are all the energy fluxes entering the atmosphere. The fluxes exiting the atmosphere are 165 W/m^2 radiated from the atmosphere to space and 324 W/m^2 radiated from the atmosphere to the surface. The total fluxes in and out of the atmosphere each total 489 W/m^2, satisfying the basic COE constraint that, in the steady-state, all the energy that enters the atmosphere must come out – either to the surface or out into space.

If ‘K’ is set to zero, this means that only 320 W/m^2 and 67 W/m^2 are inputs to the atmosphere, reducing the required output from the atmosphere by 102 W/m^2. If the surface at 288K must be receiving at least 390 W/m^2 to sustain 288K and there is only 235 W/m^2 entering post albedo, there is still enough energy input to the atmosphere to satisfy the fluxes exiting the boundaries. If 67 W/m^2 of that absorbed by the atmosphere is radiated into space as part of the 165 W/m^2 leaving, that leaves 98 W/m^2 that must be coming from some input source. If we subtract 98 from 320, we are left with 222 W/m^2, and 222 + 168 directly from the Sun = 390 W/m^2. If, on the other hand, we subtract 165 from 320, we’re left with 155, and 155 + 67 + 168 = 390. The power required to be sent out each of the boundaries to sustain the surface temperature and outgoing flux at the TOA is the same even if ‘K’ is equal to zero.

It has to be, otherwise the basic COE constraint that in the steady-state all the energy that enters the atmosphere must come out, and there are only two ways out – either to the surface or out into space, is NOT satisfied.

I should perhaps better and more clearly say that even just including the surface radiative power and post albedo solar power as inputs to the surface and atmosphere (i.e. setting ‘K’ to zero), there is still enough energy entering the atmosphere to satisfy the required power that needs to be exiting the surface and TOA boundaries in the steady-state.

You cannot have it both ways, i.e. with K = 0 and K = 102+67 W/m^2. Either one must be false. I have understood that you accept that K = 169 W/m^2 is the correct one (the value may differ a little from that, but basically this one is right).

You have presented the IR fluxes from atmosphere that correspond to this as 165 W/m^2 out to space and 324 W/m^2 down to surface. I trust that you agree that these numbers are not equal. They are not “div2”.

That’s that, you cannot have equal fluxes up and down. There’s no alternative way of looking at the radiation, the answer is unique. The supposed alternative is just totally meaningless play with numbers. You can always make up equal numbers but such artificial numbers have no relationship with what happens in the atmosphere. GW made total blunder of his derivation, you try to save it, but that’s not possible.

Yes, I accept the numbers from K&T ’97 as being roughly correct for what they are attempting to depict. Why wouldn’t I?

“You have presented the IR fluxes from atmosphere that correspond to this as 165 W/m^2 out to space and 324 W/m^2 down to surface. I trust that you agree that these numbers are not equal. They are not “div2″.

Yes of course, I agree.

“That’s that, you cannot have equal fluxes up and down. There’s no alternative way of looking at the radiation, the answer is unique. The supposed alternative is just totally meaningless play with numbers. You can always make up equal numbers but such artificial numbers have no relationship with what happens in the atmosphere. GW made total blunder of his derivation, you try to save it, but that’s not possible.”

Let me ask you this. Why does the ratio of the surface radiative power to post albedo incident solar power provide the the correct ‘zero-feedback’ calculation for 2xCO2, but the ratio of surface radiative power to the surface radiative power absorbed by the atmosphere does not? (i.e. 385/239 = 1.61, and 1.61 x 3.7 W/m^2 = 6.0 W/m^2 = +1.1C from a baseline of 287K; but 385/292 = 1.32, and 1.32 x 3.7 W/m^2 = 4.9 W/m^2, which from a baseline of 287K is only about +0.9C).

Is it pure coincidence that the former yields the exact correct answer for ‘zero-feedback’ at the surface? If the net behavior (i.e. the net flow of energy) at the boundaries depicted in GW’s simplified model was not the same as than in the real system, then the power densities of the surface and TOA should not provide the correct ‘zero-feedback’ calculation, but it clearly does. How do you explain this?

Adding CO2 leads to a temporary reduction in OLR from atmosphere to space that changes to a small addition when the new equilibrium is reached at a higher temperature of both the surface and the atmosphere. The radiation from atmosphere to space increases immediately and this increase grows with warming of the atmosphere. It’s obvious even without full calculation that there will at all stages be more addition in the radiation to the surface than in the radiation to space. At an early stage even the signs differ.

Another way of answering is that determining the changes requires estimating the new values using an approach that works for the lower concentration and calculating the difference. That leads to the result I describe above.

You propose that the increase would miraculously follow the div2 -rule in spite of the fact that you accept that it’s not valid for the whole. You have no better arguments for the increase than you have for the total. It’s as totally false than the idea that the whole would be split in two equal parts.

You may get accidentally one right value from totally false arguments. That’s not rare when the required accuracy is not very high.

The GW “theory” is throughout wrong. The only reasonable thing to do with it is to forget in in whole. More correct understanding is given by numerous textbooks and lecture texts as well as by sites like this one.

“You propose that the increase would miraculously follow the div2 -rule in spite of the fact that you accept that it’s not valid for the whole.”

No, not at all – not in the way you’re describing. Did you read no. 1 from my initial summary list? You’re responses would seem to indicate you haven’t (or didn’t fully understand it).

Y”ou have no better arguments for the increase than you have for the total. It’s as totally false than the idea that the whole would be split in two equal parts.”

In no way is GW claiming the split of the newly absorbed energy will result in an equal increase in direct radiative power from the atmosphere to the surface and from the atmosphere to space. This is at least how I am intepreting your comments. Please correct me if my interpretation is incorrect.

“You may get accidentally one right value from totally false arguments. That’s not rare when the required accuracy is not very high.”

So you’re arguing that it’s coincidence that it works out perfectly? It is also just a coincidence that the ‘zero-feedback’ Planck response at the TOA of 3.3 W/m^2 per 1C or warming can be directly derived from the global dimensionless gain ratio of 1.61 as well? (i.e. +1C from a baseline of 287K = +5.3 W/m^2 from S-B; and 5.3 W/m^2/1.61 = 3.3 W/m^2)?

It’s my understanding that the calculation of so-called ‘zero-feedback’ effectively assumes linearity between the surface and TOA power densities (even though the power densities themselves are really just taken from the non-linear average). This is a very important distinction to make, because much of what GW is doing in the div2 analysis assumes linearity upon an equilibrium state (i.e. the context is that of ‘zero-feedback’), and moreover, is why the additive superposition principle must apply to the effects of energy and power on the surface temperature.

On the other hand, if we take the ratio of gross power leaving and entering the surface of about 490 W/m^2 to that of post albedo solar power, it doesn’t provide the correct calculation of ‘zero-feedback’ (i.e. 490/239 = 2.05, and 3.7 W/m^2 x 2.05 = 7.6 W/m^2, which equals about +1.5C from a baseline of 287K).

If the calculation of ‘zero-feedback’ is not specifically based on the ratio of the surface and TOA radiative power densities, then what is it based on? How is it arrived at?

The key point that no one seems to be able to see is that temperature (i.e. the surface temperature in this case) is slaved to power in W/m^2 by the Stefan-Boltzmann Law. Specifically, it is slaved to the net power supplied to it. For example, if the surface temperature is to increase by 1.1K from 287K, the surface must be supplied with an increase in power of about 6 W/m^2. Or the surface must receive an increase of about 6 W/m^2 in net energy gained.

What complicates things is how the net energy gained at the surface is manifested by the atmosphere, and whether or not it will ultimately end up being more or less than ‘zero-feedback’ of 1.1C. If the temperature is to increase by 3C, this requires +16 W/m^2 in net energy supplied to the surface, which equals a dimentionless gain of 4.32 (16/3.7 = 4.3), which is greater than the ‘zero-feedback’ gain of 1.61, indicating net positive feedback. If the temperature is to increase by 0.8C (per L&C 2011), the net energy supplied to the surface is only required to increase by about 4.4 W/m^2, which equals a dimentionless gain of 1.19 (4.4/3.7 = 1.19), which is less than the ‘zero-feedback’ gain, indicating net negative feedback.

This forms the fundamental basis behind what GW is doing in the eb analysis and why it’s valid, but also why it’s directly applicable to how feedback is defined as being net negative or net positive in climate science.

It seems a big part of the problem is no one here has had any exposure to equivalent systems analysis via black box modeling. It’s an extremely useful methodology for analyzing the behavior of complex systems with well charaterized boundaries (i.e. where the top level constraint of COE can be clearly and easily applied). It’s ubiquitously taught in electrical engineering, but the methods are equally valid if properly applied to any system. As best I know, those who study and major in meteorology and/or atmospheric physics never have any exposure to it, and therefore, likely wouldn’t recognize or understand it.

I know my own father, who now runs his own math and physics tutoring service in retirement, had a good amount of exposure to it in his schooling years ago, which included quite a bit in EE (he was a physics major). In contrast to the replies and reactions here, when I sent him the link to GW’s div2 analysis and subsequently GW’s further attempt to clarify what he was doing (posted a JoNova and re-posted here), this was his reply:

“True to form for a system analyzer, he’s constructed a black box of the earth-atmosphere system. The boundary conditions match those of the real and much more complex system. It’s the model best suited to study feedback effects.”

In other words, the point is he immediately ‘got it’ and fundamentally understood what GW was doing. It seems no one can grasp the concept of it, as I guess it is somewhat counter intuitive in that what you’re looking at via the black box model isn’t what is actually happening – only that the net effect or net flow of energy at the boundaries is the same as if it was what was actually happening. This seems to just blow everyone’s mind and/or totally fake everyone out.

It seems a big part of the problem is no one here has had any exposure to equivalent systems analysis via black box modeling..It seems no one can grasp the concept of it.. This seems to just blow everyone’s mind and/or totally fake everyone out.

The problem is not that no one understands black box modeling, the problem is that your calculation is invalid.

Many people have explained this to you. I know you can’t understand how to apply the first law of thermodynamics or how to write down a set of equations and I now have less than zero interest in trying again.

However, let’s work on that basis that we pretend your confident statement is true, our minds are blown, we just can’t get the huge paradigm shift of equivalent systems analysis (along with the entire world of professors of physics who’ve studied and taught atmospheric physics for decades) and you sigh and give up posting comments on this subject on this blog.

You have posted many hundreds of comments all saying exactly the same wrong stuff in almost exactly the same words and unless others who read or comment on this blog have a huge fascination with misapplications of how to equate Energy In to Energy Out for a body – I am feeling like I should just delete further comments from you.

You’ve had your say and maybe it’s time to hang up your debating shoes and let other topics get discussed.

As best I could tell, Pekka and myself were having a cordial exchange with each other. He is responding to my comments and vice versa. I only reluctantly started discussing this again because Dewitt, much to my surprise, agreed that the 3.7 W/m^2 was just the net absorption increase. In my experience, most people overtly disagree with this for a variety of reasons. Notice also that my discussion with Dewitt eventually ran its course and is effectively over now (as best I can tell).

If you’re so confident that everything I’m saying is flat out wrong (which you seem to be), then why is it a problem if the discussion is in accordance with the Etiquette standards and goes on a bit longer? Why not let me serve as a model for someone who is supposedly clueless, doesn’t understand how COE applies to the boundaries, etc., but thinks he’s so right. Moreover, why not let the discussion serve as a model for how to systematically reply to the uneducated and uninformed, so others will be ‘properly’ educated and not led down the same ‘wrong’ path put forth by GW?

I respect that it’s your blog and you can do what you want with it. If you’re overtly asking me to stop, then I guess I will, but I have to be honest and say I think such a request is unjustified and really not fair (i.e. not objective) in this case.

Also, the exchange between Pekka and I was effectively re-started because I finally went back, as indirectly requested, and got the equations GW is using and posted them. He responded to that and subsequent replies between us followed. Since you’re always accusing me of not supplying equations in suppport of the things I’m saying, which is plenty fair enough, why don’t you comment on GW’s equations and explain why they are ‘wrong’?

“However, let’s work on that basis that we pretend your confident statement is true, our minds are blown, we just can’t get the huge paradigm shift of equivalent systems analysis (along with the entire world of professors of physics who’ve studied and taught atmospheric physics for decades) and you sigh and give up posting comments on this subject on this blog.”

Not a bad summation. I would only add that I don’t think anything that GW is putting forth overtly conflicts with what is already known about the physics of the atmosphere, but rather a lack of fundamental understanding of what GW is doing is being misinterpreted as overtly conflicting with what is already known about the physics of the atmosphere. I would say this especially applies to what’s in the eb analysis regarding climate sensitivity, which ultimately is really basic stuff that’s not at all difficult to understand (or shouldn’t be). div2 is a bit more involved, but ultimately is based on the same fundamentals. div2 and the halving of the 3.7 W/m^2 aside, that apparently no one in the entire atmospheric science community can understand what GW is doing in eb and why it’s valid, IMO, is pretty sad.

It also seems part of the problem is GW has different meanings for certain terms compared to how they are defined and used in atmospheric science. For example, GW says:

“This means that 1 watt of surface forcing will result in about 1.6 watts of post feedback, steady state, surface power when integrated over a year.”

What GW means by ‘surface forcing’ in this context here is post albedo solar or equivalent forcing. It seems many misinterpret this as somehow meaning the net absorbption increase that occurs at or just above the surface level, as defined in atmospheric physics (I don’t know the exact definition)

Another problem seems to be that GW has a different meaning for the term ‘radiative balance’ than how it’s used in atmospheric science. What GW means by the ‘radiative balance’ is just pure radiative balance at the TOA and steady radiative flux from the surface (sustained by steady net energy flow supplied to the surface). I’ve noticed in many instances where this has caused massive confusion, since of course in the real system there is no pure radiative balance at the surface, because the surface is convectively coupled to the atmosphere.

I asked once that you write up definitions of your concepts, assign letters for them and write the full set of equations that you base your arguments on. You have not done anything like that. You continue to write lengthy messages telling, how you don’t ever mean what others have found from your earlier messages. You mean something else that we stupid individuals don’t understand and then you insist that others answer to questions that cannot be answered as long as there is no common understanding on the definition of the concepts.

So once more: Define your concepts in a way that allows others to understand what you are talking about.

I got back to the discussion when I looked at the div2-paper and realized how terribly wrong it was. I hoped that pointing that out to you would finally make you realize that your theories are simply wrong. The gross error was easy to see when GW defined concepts and wrote equations. You don’t even try to do that.

Now you write that GW was not discussing the same balance as we others. Perhaps so but then his own balance has nothing to do with the FIrst Law except that it’s not possible to satisfy his balance without gross violation of the First Law. His alternative balance is not a balance of the real atmosphere. The real atmosphere has an energy balance that takes into account all forms of energy, no balance exists for IR separately.

I have not found any single valid idea in any of your messages (except of course in those sentences where you accept main stream observations).

As I’m as unsuccessful as everybody else in making you realize where your thinking fails I give up (again). I don’t think that arguing with you further produces anything helpful for anybody trying to learn valid understanding.

I really wish that the next comment that I see from you contains the definitions and equations I have been asking for. Thus I hope that you don’t write more comments until you have got that far, or until you switch your approach to one of trying to learn proper physics and other proper understanding of atmosphere.

The idea of this site is understanding the valid science basis. Discussing alternative approaches serves often that purpose. That may lead to new and at least in some way better explanations of the science. There are also less common but equally valid formulations of the basic physics and discussing them opens new perspectives.

Discussing one specific set of misconceptions is, however, not useful forever. At some point it’s better to stop that. Discussing your ideas has reached that point already several times. Coming back to them time after time has not produced anything of value and will not produce until you are ready to do your part in a very different way. I don’t expect that to happen but with good will you might be able to make a new better start.

“…the calculation of emission and absorption of radiation from the atmosphere does not use the Stefan-Boltzmann equation. When you find this equation used in introductory atmospheric physics textbooks it is to provide simple teaching examples. If only people read to the end of the textbook.. See, as an example, Simple atmospheric models part 1″

That post includes this statement:
“For any real surface (or body of gas) this Planck curve is multiplied by the emissivity curve (vs wavelength) to get the actual thermal emission vs wavelength.
To calculate the flux (W/m²) we can instead use the Stefan-Boltzmann equation (which is just the integral of the Planck curve over all wavelengths):
E = εσT4
where E = energy emitted in W/m², ε = emissivity, σ = 5.67 x 10-8, T = surface temperature”

Is the student not entitled to read equivalence of outcome between the complex and the simple treatments?

Understanding Atmospheric Radiation and the Greenhouse Effect Part 1 includes a statement:

“The theory about emitted radiation
E = εσT4
– is a solid theory, backed up over the last 150 years”.

Later it includes a figure depicting an atmospheric horizontal layer with arrows labeled “Emitted radiation” issuing from both surfaces, pointing upwards from the upper surface and downwards from the lower one.

Is the student not entitled to read equivalence between the formula and the label?

This, apparently, is what Hartmann does in Fig 3.10 Diagram of simple two-layer radiative equilibrium model for the atmosphere-Earth system, showing the fluxes of radiant energy, in which S-B appears expressly.

That’s Dennis L Hartmann in the Department of Atmospheric Sciences, University of Washington whose textbook Global Physical Climatology I acquired on your recommendation, unqualified as I recall.

When Hartmann writes “Readers not interested in the details of infrared radiative transfer in the atmosphere may skip ahead to……..where simple heuristic models are described” may not the student infer practical equivalence between the complex and the simple?

I don’t think you are able to grasp this subject. I’m pleased that you bought Hartmann but he’s not for everyone.

You cite the example (shown in his fig 3.10) he uses to show how temperature increases with simple atmospheric layers (“shell model”) where the layers are blackbodies in the longwave.

a) This proves your point that climate scientists are misleading people?

b) Or it proves my point that people who read books need to read the whole chapter?

c) Or assuming that you did read the whole chapter, demonstrates that climate science isn’t a subject for everyone?

Here is a little bit from that very same chapter:

and later..

i) Hartmann understands the subject
ii) Hartmann doesn’t believe that the atmosphere emits as a blackbody and
iii) the reason he uses a simple model at some point in an introductory text is as a conceptual primer

If you think myself, Pierrehumbert and Hartmann teach that the atmosphere radiates as a blackbody then there is no point in trying to explain anything to you.

None of a, b or c. We got onto this track when I responded too quickly and carelessly to DeWitt’s comment about S-B. For this I apologise. My purpose was defensive in citing your work and Hartmann. Collectively, IMO, they encourage students to see equivalence in the simple and the complex treatments.

I don’t think that I am confusing micro and macro ideas: rather I think I see different outcomes between them, most likely because I don’t understand one or the other. As you say the idea of an effective emission altitude can give a false picture of reality. Emission and absorption occur everywhere in the atmosphere. Emission and absorption of EM radiation are what individual radiatively-active molecules do. An individual molecule doesn’t do both simultaneously, different molecules at the same LTE are involved. Because emission and absorption occur at the same LTE, they must be equal. This result is independent of the number of active molecules in the thin layer for which LTE remains constant. In other words a higher population of active molecules in each thin layer still emit as much as they absorb. You say differently: “If the atmosphere contains more absorbers then the solution to the radiative transfer equation is less emission”. This is the difference I wish to understand.

For a given wavenumber, v, the absorption of radiation is dependent on the amount of incident radiation at wavenumber v and the number of absorbers at that wavenumber.

The emission of radiation at wavenumber, v, is dependent on the temperature of the gas in that portion of the atmosphere, the Planck function at that temperature and wavenumber and the number of absorbers at that wavenumber.

In a gas, the redistribution of absorbed energy occurs by various types of collisions between the atoms, molecules, electrons and ions that comprise the gas. Under most engineering conditions, this redistribution occurs quite rapidly, and the energy states of the gas will be populated in equilibrium distributions at any given locality. When this is true, the Planck spectral distribution correctly describes the emission from a blackbody..

..And an explanation about where LTE does not apply might help illuminate the subject, from Siegel & Howell:

Cases in which the LTE assumption breaks down are occasionally encountered.

Examples are in very rarefied gases, where the rate and/or effectiveness of interparticle collisions in redistributing absorbed radiant energy is low; when rapid transients exist so that the populations of energy states of the particles cannot adjust to new conditions during the transient; where very sharp gradients occur so that local conditions depend on particles that arrive from adjacent localities at widely different conditions and may emit before reaching equilibrium and where extremely large radiative fluxes exists, so that absorption of energy and therefore populations of higher energy states occur so strongly that collisional processes cannot repopulate the lower states to an equilibrium density..

To me it seems that this latest apparent disagreement is not real but only about misunderstanding what the other is saying.

Equation (3.29) in the chapter from Hartmann’s book SoD presents in one of his comments tells the condition for equal emission and absorption for one wavelength and one direction of radiation. If the radiation intensity I as defined by Hartmann is equal to the value B given by Plank’s law then the difference is zero and emission equals absorption locally.

For upwards radiation the intensity I is almost always larger than B, because I is in balance at a higher temperature of lower altitude (typically at the distance determined by the penetration depth or mean free path). Being in balance with a higher temperature means that intensity is higher. Therefore the formula (3.29) tells that the intensity gets reduced the faster the larger the density of CO2 is. This is the reason for the negative influence of added CO2 for the OLR.

When SoD wrote “If the atmosphere contains more absorbers then the solution to the radiative transfer equation is less emission” that was not about local equilibrium but about the OLR at the top of the atmosphere. Thus this sentence of SoD refers to the total influence of the effect I mention in the above paragraph taking all upwards directions all IR wavelengths into account.

In eqn 3.29, dI = 0 by construction; consequently I = B. But you say that for upwards radiation generally I exceeds B because it reflects the higher temperature at a lower altitude. I take this to mean that at any “z” I(z) = B(z) always and that in the troposphere B(z-dz) is generally greater than B(z); therefore I(z-dz) must exceed B(z) and dI must be negative, reflecting attenuation. LTE is maintained at z: I(z-dz) – dI = I(z) = B(z).

By eqn 3.29, attenuation varies directly with the density and coefficient of absorption of the active molecules. Adding active molecules increases their density and attenuation effect, -dI, at any altitude. It also increases the amount of attenuation from the surface to any altitude. At some density of active molecules in the atmosphere the amount of attenuation results in OLR which just balances incoming solar. Adding active molecules, by increasing attenuation, results in OLR less than needed for that balance. I think I’ve understood you correctly.

From here the conventional view seems to be that to restore balance, the system, including the surface, must warm in order to increase the strength of emission. But how does it warm – solar input hasn’t changed? In fact it is already warmed by the process we have been discussing. The cumulative attenuation, heat retained in the system, is the other side of the flux imbalance at TOA. Does this mean automatic negative feedback? No. The attenuation discussed here would occur at any temperature profile in the system. That is, the system would continue to warm – a runaway greenhouse effect? No, a countervailing process within the system heads that off.

Return of solar energy thermalised at the surface to space by attenuated radiative transfer through the atmosphere is a relatively minor component of the total cycle. Return by mass transport to the upper troposphere for radiation to space is the major component. In this process increasing the density of active molecules, or emissivity, enhances radiation to space, cooling the system.

In the first half of your comment you describe correctly many parts of my comment, but not quite accurately.

Looking separately intensities of upwards (Iu) and downwards (Id) radiation we have at every altitude Iu(z) > B(z) and Id(z) < B(z). The difference is small at the absorption peak near 15 µm but larger at other wavelengths due to the different mean free paths of each wavelength. It’s also true that Iu(z) + Id(z) > 2*B(z), but this difference is much smaller.

Your comment is more or less correct up to the last sentence where you contradict both my comments and the first half of your own comment. You write there that more active molecules enhances radiation to space while it was just concluded that more active molecules reduces the radiation to space rather than enhances it.

More molecules reduce the radiation to space, because they lead to a reduction in the upwards flux. They block more radiation that would otherwise escape than they emit themselves. That was the point in observing that (3.29) gives a negative value for upwards flux and the more negative the higher the density of CO2.

The apparent contradiction in the last sentence of my comment is explained by the big difference between energy transport by mass transfer and by radiative transfer. Although mass transfer must give way eventually to radiative transfer to space, this occurs high in the troposphere. As I understand the meteorology, latent heat of vapourisation is carried upwards by convection of moist air until the moisture precipitates; and latent heat converts to sensible heat which propels the now dry air higher into the atmosphere where CO2 is the main active molecule and radiative transfer takes over. Cumulative attenuation over this much shorter path would be much less than over the path originating at the surface. That would seem to suggest that whereas adding active molecules would enhance warming in the latter case it would enhance cooling in the former.

John,
What you are describing is lapse rate feedback or at least closely related to that. The lapse rate feedback is a negative feedback as you describe. It’s a true effect and it cancels part of positive water vapor feedback. The strengths of these two feedbacks are correlated as both depend on the moisture level. The overall effect turns out to be positive, i.e. the additional GHE produced by more water vapor is stronger than the increase in OLR due to warmer upper troposphere.

This is not a direct consequence of fundamental principles but observed in comparison of results obtained from different models.

dTs = Ts/4*(dE/E), where Ts is equal to the surface temperature and dE is the change in emissivity (or change in OLR) and E is the emissivity of the planet (or total OLR). Sorry if my algebraic formulation is not entirely correct, as it’s been many years for me.

Plugging this in we get dTs = 287K/4 * (3.7/239) = 1.11K

Now, can someone explain to me where non-radiative flux from the surface, designated as ‘K’ by SoD, is involved in this calculation (to ensure COE is properly applied to the surface and TOA boundaries)? My point of contention now for a very long time is that it’s not involved, because the concept of ‘zero-feedback’ assumes no changes in ‘K’, which particularly applies to no. 8 of my initial summary list.

Also, can someone explain why if we multiply 3.7 W/m^2 by the global dimentionless gain ratio of 1.61 and add it to the baseline of 287K, it also yields +1.11K? The only answer I’ve gotton so far is that it’s just a coincidence.

dTs = Ts/4*(dE/E), where Ts is equal to the surface temperature and dE is the change in emissivity (or change in OLR) and E is the emissivity of the planet (or total OLR).

I don’t know why I bother, but here it is anyway:

I love the way you mix and match numbers. 3.7 W/m² for doubling CO2 does not apply to the surface and never has. It’s defined at the tropopause only and then only after the stratosphere has been allowed to equilibrate. Ts, then, is not the surface temperature, it’s Teff at the tropopause which is ~255 K, not 287 K. Also, since some solar radiation is absorbed by the stratosphere and radiated to space, it’s not 239 W/m² either, but somewhat less. But ignoring that, the highly simplified calculation is that a change of 3.7 W/m² at the TOA produces a no-feedback change of 0.99 K while a change of 0.99 K at a surface temperature of 288 K produces a flux change of 5.4 W/m² at the surface, not 3.7 W/m².

And yes you can sort of ignore convective energy transfer from the surface to the atmosphere when calculating no-feedback ΔTsurface. But, as far as I can tell, you take that to mean you can always ignore it when calculating energy balances, leading to underestimating the total absorption of energy by the atmosphere, for example. And even in the no feedback case, K is not a constant because the emission from the atmosphere absorbed by the surface changes at a different rate with temperature than emission from the surface that is absorbed by the atmosphere, assuming that ΔTsurface = ΔTtoa.

Simply: Increasing CO2 reduces the amount of energy transmitted to space by the surface. To maintain energy balance, K must increase to make up the difference. That’s not exact because the ratio of surface up absorbed to surface down radiated changes slightly too, but it’s a good first approximation.

Now you have me thoroughly confused. When did I ever say or imply that the 3.7 W/m^2 ‘applies to the surface’? It’s the net absorption increase. The 3.7 W/m^2 includes the so-called ‘stratospheric adjustment’, which means it can be considered to be that through to the TOA (at least according to Myhre). Now we disputed earlier whether or not the 3.7 W/m^2 is all surface radiative power newly absorbed or whether it includes reduction in emission to space from that which is radiated from the atmosphere itself, but this doesn’t seem to be what you’re getting at.

The calculation of ‘zero-feedback’ is change in temperature the surface not the TOA, right? That is, the surface temperature is supposed to increase by about 1.1C from an additional 3.7 W/m^2 of atmospheric absorption, right?

You seem to be saying that a flux decrease of 3.7 W/m^2 at the TOA or tropopause level reduces the effective radiating temperature of the planet by about 1K. I haven’t checked your calculation, but I certainly don’t dispute this. You then say that +1K at the surface increases the radiative flux by 5.4 W/m^2, which again I certainly agree with.

“And yes you can sort of ignore convective energy transfer from the surface to the atmosphere when calculating no-feedback ΔTsurface.”

My point is it’s not involved in the ‘zero-feedback’ calculation, and doesn’t need to be in order for COE to be properly applied to the surface and TOA boundaries. As I’ve interpreted SoD, he is saying that it does, and is why GW can’t assume that the net effect at the boundaries is the same as if ‘K’ is equal to zero. I’m saying if this wasn’t correct, than using the dimensionless gain ratio to calculate ‘zero-feedback’ as I’ve done wouldn’t provide the same (correct) answer, but it does. Such is the whole point of a so-called ‘equivalent’ black box model (i.e. it still arrives at the correct answer even though its not modelling the actual behavior).

“But, as far as I can tell, you take that to mean you can always ignore it when calculating energy balances, leading to underestimating the total absorption of energy by the atmosphere, for example.”

No, I’m certainly not saying this. Absolutely it cannot be ignored when calculating how a change in absorbtion subsequently changes ‘K’, which then subsequently changes absorption and ‘K’ further, eventually leading to a new equilibrium surface energy balance.

“Simply: Increasing CO2 reduces the amount of energy transmitted to space by the surface. To maintain energy balance, K must increase to make up the difference. That’s not exact because the ratio of surface up absorbed to surface down radiated changes slightly too, but it’s a good first approximation.”

I wouldn’t disagree with this. I understand that the amount of ‘K’ is tied to the surface temperature (especially for the latent heat of evaporation). That is, if the surface temperature increases, ‘K’ would also increase by some amount. I further understand that an increase in ‘K’ would also result in an increase in dowward LW from the atmosphere to the surface (at least as a first order approximation).

OK, I did finally hear back from Gunnar Myhre and he says he made a mistake and the 3.7 W/m^2 does include reduction in emission to space from that radiated from the atmosphere itself.

So it appears then the quantification of 1.1C of ‘zero-feedback’ at the surface from the +3.7 W/m^2 of atmospheric absorption from 2xCO2 being equal to +3.7 W/m^2 of post albedo solar power is solely because the two are equal to one another on an energy quantitative basis? Is this correct?

If yes, then I would still maintain that this is weak and doesn’t really add up and make complete physical and logical sense given the fundamental mechanism of the GHE is the absorption of upwelling radiation that is subsequently re-radiated back downwards.

I admit I was wrong on the calculated 3.7 W/m^2 and now see the whole thing as clear as day. Obviously I’m embarrassed for making such an oversight and error all this time (and feel foolish). While I can partly blame Myhre for mistakenly confirming it, I still should have fully investigated it first hand and made sure I understood exactly how it was being arrived at (and what it was a measure of) before I started trying to apply it to what GW or anyone claiming anything ‘new’ was putting forth. I get it – the calculated 3.7 W/m^2 is derived from a multi-layered atmospheric radiative transfer model that accounts for changes in both upwelling and downwelling radiation through the whole atmosphere (not just the surface => TOA component), where for 2xCO2 the calculated 3.7 W/m^2 is the reduction in the total outgoing LW flux at the TOA and the corresponding increase in upwelling LW flux absorbed by the atmosphere.

It turns out GW is not claiming otherwise, as I had mistakenly thought the ‘T’ component of his model and analysis was modeling the actual behavior, but it isn’t. I apologized to GW for misrepresenting his work all this time.

All of this being said, as best I know, the same principle (as I had been prior applying it) still applies to the newly absorbed energy none the less, and I think I may still see and understand the claimed equivalency, though I would be interested to see specifically how GW himself explains it.

My understanding of the way +1.1C of ‘zero-feedback’ at the surface is arrived at for +3.7 W/m^2 of post albedo solar power is to take the dimentionless ratio of the surface and TOA power densities, which is 1.61 (385/239 = 1.61, where at 287K the surface is supplied with net of about 385 W/m^2 and 239 W/m^2 is the post albedo solar power entering the system and the LW flux exiting the system at the TOA), and then multiply it by the 3.7 W/m^2 and then add the result back to the baseline of 385 W/m^2 and convert back to temperature. That is, 1.61 x 3.7 W/m^2 = 6.0 W/m^2, and 385 W/m^2 + 6.0 W/m^2 = 391 W/m^2 = 288.1K (or +1.1C). (*this is effectively all Arrhenius and similar formulas are doing with the 3.7 W/m^2 from 2xCO2 to arrive at 1.1C).

What I don’t understand is why it intuitively makes sense or seems valid to you to do the same for +3.7 W/m^2 of GHG absorption, given the fundamental mechanism for how GHGs elevate the surface temperature above what it would be in their absence is the absorption of upwelling radiation acting to cool that is absorbed and subsequently re-radiated back downwards, thereby increasing radiative resistance to cooling; and specifically not via some sort of conduction process. Every description or definition of the GHE, including that from the IPCC, uses phrasing very similar to this one from Wikipedia:

“The greenhouse effect is a process by which thermal radiation from a planetary surface is absorbed by atmospheric greenhouse gases, and is re-radiated in all directions. Since part of this re-radiation is back towards the surface and the lower atmosphere, it results in an elevation of the average surface temperature above what it would be in the absence of the gases.”

Each layer of the atmosphere that absorbs upwelling radiation subsquently radiates that absorbed energy both up and down. I fail to understand how this somehow wouldn’t have to be accounted for in the calculation of ‘zero-feedback’ at the surface from incremental GHG absorption. I mean it would be one thing to question and/or not understand that it’s claimed to be virtually exactly half – given the lapse rate, the large amount of convective flux, the non-linearity of all the effects, etc., but another to somehow think it should be considered exactly equal to additional solar forcing. This is what puzzles me. Why does the atmospheric science community think that for the calculation of ‘zero-feedback’ at the surface it does not have to be accounted for that the atmosphere radiates its absorbed energy both up and down? Is absorbed radiative energy re-emitted up in the atmosphere not part of the radiative cooling process in the system (i.e. in the act of cooling and not warming)?

To me, if the 3.7 W/m^2 is just a quantification of the reduction in upwelling radiation that was all prior passing out to space and not a quantification of 3.7 W/m^2 in the act of radiating downward (or more specifically back downward), I don’t understand how it can be considered equal to 3.7 W/m^2 of additional post albedo solar power which is all in the act of radiating downward (i.e. a continuous stream of downward radiated energy flowing into the whole Earth-atmosphere system, all in the direction toward the surface). I’m perplexed why even in light of this you appear to think it is still valid to consider them equal to one another.

Specific mechanisms are less important than the overall balance. If energy in and energy out are equal, then you have steady state and there is no change in system energy content. If energy in is more than energy out, energy will accumulate in the system and temperatures will go up. In terms of total energy accumulation, it doesn’t matter if the imbalance is caused by an increase in energy in or a decrease in energy out. It does matter for the specific details of the transition to the new steady state, i.e. what temperature goes up first, but the new steady state will look about the same no matter how it got there.

I’m not disputing the basics that the -3.7 W/m^2 at the TOA will require the atmosphere and ultimately the surface to warm in order to re-establish equilibrium with space. The issue is specifically the calculation of so-called ‘zero-feedback’ at the surface required to re-establish energy balance (i.e. in the absence of feedback).

If there were one simple question that gets to the whole point in contention here it would be the following:

For the calculation of 1.1C of ‘zero-feedback’ at the surface, how has it been accounted for that the atmosphere radiates its absorbed energy both up and down?

Can you (or anyone) explain and/or quantify how this has been acounted for in the arrived at 1.1C?

I plan to do something like that in a while. We just keep the lapse rate and the absolute water vapor concentration constant, allow the surface to heat up, and let the model run to equilibrium.

If you can understand what that model is doing with up and down fluxes (well spectra, as we are considering each wavelength individually) you should be able to see how we can find the new temperature needed.

In brief, let’s say that the surface temperature shown in the simulation run for 280 ppm is an equilibrium value (it’s not), then when we double CO2 concentrations there ends up being a radiative imbalance at top of atmosphere. Keep increasing surface temperature (with lapse rate and water vapor held constant) and eventually the net imbalance disappears. And yes the model has the atmosphere radiating up and down.

If you are unclear try and explain which bit is unclear –

– the current model doesn’t account for up and down fluxes?
– the model doesn’t produce a net imbalance at TOA when CO2 concentrations increase?
– increasing surface temperature doesn’t change these up and down fluxes?

“We just keep the lapse rate and the absolute water vapor concentration constant, allow the surface to heat up, and let the model run to equilibrium.

If you can understand what that model is doing with up and down fluxes (well spectra, as we are considering each wavelength individually) you should be able to see how we can find the new temperature needed.

In brief, let’s say that the surface temperature shown in the simulation run for 280 ppm is an equilibrium value (it’s not), then when we double CO2 concentrations there ends up being a radiative imbalance at top of atmosphere. Keep increasing surface temperature (with lapse rate and water vapor held constant) and eventually the net imbalance disappears. And yes the model has the atmosphere radiating up and down.”

Yes, but the atmosphere would warm first – not the other way around, right? For this to be an accurate run of what would actually happen, it would have to simulate the atmosphere warming first, as it would in the real system. Moreover, even if so, I would definitely need to see that the fundamental dynamic of the energy transfer of the model run is simulating and is consistent with the definition of the fundamental mechanism driving the GHE (i.e. via downward re-radiation of the newly absorbed energy) and not simulating energy transfer through the atmosphere primarily via a conduction process. This is very important, because if the simulated dynamic is not primarily transferring energy by radiation, it would not be simulating the same behavior as that which would occur in the real atmosphere.

I assume we agree that the overwhelming way energy is transferred from the atmosphere to the surface is via radiation and not conduction, right? I assume this since it is universally agreed in atmospheric physics that the surface receives much more direct radiative power from the atmosphere and Sun that it emits, and there is net non-radiative loss from the surface to the atmosphere.

I agree the process you’ve laid out above would work to restore balance. I just don’t think it’s an accurate way to simulate what would actually happen, and thus wouldn’t seem to adequately address or resolve the fundamental issue in contention here.

Temperature is a state function in thermodynamics. That means the path to get from one temperature to another doesn’t matter. What you appear to be worried about are the details of the path. That’s a separate subject that would fall under the topic of modelling. But nobody is going to actually model a step change since that is not relevant to the current situation. What’s usually done is to increase CO2 at some rate until the concentration is doubled and then stop, a ramp rather than a step. As I remember, the way it’s usually done is to raise the CO2 concentration by 1%/year for 70 years. Even that is faster than CO2 is actually going up, but not by all that much. But the models all include feedbacks.

For the calculation of 1.1C of ‘zero-feedback’ at the surface, how has it been accounted for that the atmosphere radiates its absorbed energy both up and down?

The 1.1 C calculation isn’t about the energy balance at the surface. It’s the change in the surface temperature required to achieve radiative balance, specifically (LW + SW reflected) up – (SW + LW) down at the tropopause after the stratosphere is allowed to equilibrate assuming nothing else, like lapse rate, humidity and cloud cover is allowed to change. LW down at the tropopause can be ignored because after allowing the stratosphere to equilibrate, it shouldn’t change, similarly for SW reflected. It says nothing about energy balance at the surface or anywhere else. It’s simply an approximation to get a ballpark figure. To repeat, it’s an approximation. Spending a lot of time on the details of how it’s calculated or exactly what it means is pointless.

It’s also something like calculating the magnitude of the greenhouse effect on the Earth. There are all sorts of approximations one can use, the classic being an isothermal sphere with the same albedo which gives you the lower limit for the magnitude. But they’re all approximations with limited utility. Which means they’re all wrong in at least one respect. Worrying about the details of the calculation is nugatory.

Yes, but the atmosphere would warm first – not the other way around, right? For this to be an accurate run of what would actually happen, it would have to simulate the atmosphere warming first, as it would in the real system.

DeWitt’s point of January 13, 2013 at 8:53 pm is correct.

If mystically the surface temperature gets raised to a new value and we find as a consequence that an imbalance from adding CO2 has gone to zero then we know that is the new (no feedback) equilibrium temperature.

However, one of the objectives of the Visualization series and of the model is to allow people to see the mechanisms in action, see see how energy moves through the atmosphere and surface.

Moreover, even if so, I would definitely need to see that the fundamental dynamic of the energy transfer of the model run is simulating and is consistent with the definition of the fundamental mechanism driving the GHE (i.e. via downward re-radiation of the newly absorbed energy) and not simulating energy transfer through the atmosphere primarily via a conduction process…

Amazingly, the mechanisms behind the model are consistent with the mechanisms behind the GHE. There’s radiation and there’s convection (this is modeled very simplistically via ensuring the environmental lapse rate never exceeds the “prescribed lapse rate”, more on this later).

Think of it a bit like the point of Part Three – Average Height of Emission. There is no one height of emission to space, there is a spectrum of values from every height. But we use the term “average height of emission getting raised to a higher and colder point” as an over-simplification to convey the idea.

When GHGs are added to the atmosphere there is a spectrum of changes that take place.

How we summarize the end result is always an over-simplification of the sum of all the mechanisms.

“The 1.1 C calculation isn’t about the energy balance at the surface. It’s the change in the surface temperature required to achieve radiative balance,”

Yes, +1.1C at the surface would restore radiative balance at the TOA, but +1.1C at the surface isn’t necessarily required to restore radiative balace at the TOA. This is the whole point. The only requirement to restore radiative balance at the TOA is (as you say) for LW out to equal SW in. That’s it.

“specifically (LW + SW reflected) up – (SW + LW) down at the tropopause after the stratosphere is allowed to equilibrate assuming nothing else, like lapse rate, humidity and cloud cover is allowed to change. LW down at the tropopause can be ignored because after allowing the stratosphere to equilibrate, it shouldn’t change, similarly for SW reflected. It says nothing about energy balance at the surface or anywhere else. It’s simply an approximation to get a ballpark figure. To repeat, it’s an approximation. Spending a lot of time on the details of how it’s calculated or exactly what it means is pointless.

It’s also something like calculating the magnitude of the greenhouse effect on the Earth. There are all sorts of approximations one can use, the classic being an isothermal sphere with the same albedo which gives you the lower limit for the magnitude. But they’re all approximations with limited utility. Which means they’re all wrong in at least one respect. Worrying about the details of the calculation is nugatory.”

I very much disagree. The reason why it is so absolutely critical is because ‘zero-feedback’ is the baseline from which net feedback and the resulting final temperature change at the surface is specifically derived from. Additionally and just as vital, it is a measure of the instrinsic effect on the surface temperature subsequent absorption from feedback processes such as water vapor and clouds would be considered to have that would further amplify (or attenuate) the warming effect from doubled CO2 alone. So the significance, if there were any kind of error or inaccuracy, would extend well beyond just the so-called ‘zero-feedback’ response at the surface from a doubling of CO2.

Plus, the so-called magnitude of the GHE on Earth that you speak of (i.e. the net increase in temperature and energy supplied to the surface) as a result GHGs being in the atmosphere is only about an additional 150 W/m^2 (or +33C). The RT calculation that arrives at +3.7 W/m^2 of atmospheric absorption from 2xCO2 – what is the total absorption the 3.7 W/m^2 is an increase from? I bet it’s much more than 150 W/m^2.

“If mystically the surface temperature gets raised to a new value and we find as a consequence that an imbalance from adding CO2 has gone to zero then we know that is the new (no feedback) equilibrium temperature.”

But why? I’m not following the logic here (physical or othewise). All what you’re saying would show is *if* the surface temperature were to increase by 1.1C (independent of mechanism) it would restore radiative balance for both +3.7 W/m^2 of post albedo solar power and +3.7 W/m^2 of GHG absorption (which I agree with). In no way does this prove or demonstrate that +1.1C at the surface (for no feedback) is itself a requirement to restore balance at the TOA from +3.7 W/m^2 of GHG absorption. This is because you’ve made no accounting for cause and effect – you’ve only shown that the outcome of one potential effect (i.e. +1.1C at the surface) would restore balance at the TOA.

The no-feedback surface warming is not used in any serious calculation as input or even as a property of an intermediate state in the analysis. It has only illustrative value. It’s not a property of real Earth or of any climate model that is set to describe real Earth. There isn’t any way that no-feedback temperature change can be observed, not even under unrealistic assumptions like adding suddenly a lot of CO2 to the atmosphere.

What it is, is only the result of calculations done according to certain non-realistic rules. It’s again one of those numbers I call curiosity values. It’s defined essentially as follows:

1) Add suddenly CO2 to the atmosphere.

2) Let stratosphere settle to a new balance.

3) Force the temperature of the surface and the temperature profile of the troposphere to change disallowing all changes in the humidity, lapse rate and cloud albedo.and requiring that the change is such that the net radiative flux at TOA is zero again.

The no-feedback warming is the calculated warming of the surface when all the above is done.

The two first points are possible in principle, the third one is not. Therefore it’s not a property of the real Earth system. Climate models can be forced to calculate that value, when the feedbacks are disallowed, but this is a mode are used only to calculate this value or some other values to serve as a reference in comparisons.

When the climate models are used to make more realistic calculations the no-feedback warming is not used as input but the the input comes from the more basic changes like forcing.

It’s important to note that all the 1.6 to 1 power densities ratio between the surface and the TOA used to arrive at 1.1C (i.e. via Arrhenius) really only validates the T^4 dependence between temperature and power (i.e. specifically the difference between the surface and TOA). That’s pretty much it. It implicitly says nothing about how a change in absorption by GHGs, in the absence of feedback, should subsequently change the emissivity of the planet, yet this is what is being assumed (arbitrarily and incorrectly I argue).

In short, if variable e is the planetary emissivity, it’s not valid to claim dependence on e soley do to the T^4 relationship between temperature and power (at the surface and TOA), because e itself is independent of this relationship.

The emissivity of the planet is about 0.62 (239/385 = 0.62), where the inverse is 1.61 (1/0.62 = 1.61) and the difference is 146 W/m^2, which is different (and smaller) than 239 W/m^2.

I understand that the concept of zero-feedback is only theoretical (i.e. doesn’t exist in a real or directly measurable sense). None the less though, it is a measure or calculation of the ‘instrinsic’ effect additional GHG absorption is supposed to have in raising the surface above what it would otherwise be; thus, the significance of its accuracy and absolute correctness is enormous.

The IPCC’s nominal estimate of +3.3C for the equilibrium sensitivity for 2xCO2 is specifically derived from a 1.1C ‘zero-feedback’ baseline, is it not?

The models have no separate assumption on that. Depending on their details that either does follow from their other assumptions or that’s not exactly true in a model that considers the changes in more detail taking geographic distribution into account.

“The models have no separate assumption on that. Depending on their details that either does follow from their other assumptions or that’s not exactly true in a model that considers the changes in more detail taking geographic distribution into account.”

Is it fair to ask how you believe you know this to be the case? While I know the actual physical response itself is modelled different for additional solar than it is for additional GHG absorption (due to a lot of the additional solar going directly to the surface as SW), this doesn’t necessarily mean the ‘instrinc’ effect on raising the surface temperature of each isn’t assumed or comes out to be the same.

“The emissivity of the planet is about 0.62 (239/385 = 0.62), where the inverse is 1.61 (1/0.62 = 1.61) and the difference is 146 W/m^2, which is different (and smaller) than 239 W/m^2.”

I should have added here that the difference of 146 W/m^2 is specifically not a quantification of total GHG absorption, where as 239 is specifically a quantification of total incident post albedo solar power; thus, incremental GHG absorption’s effect on the surface temperature, for ‘zero-feedback’, is itself in no way dependent on the ratio of the surface and TOA power densities (i.e. the 1.6 to 1 ratio). Yet this is specifically what is being arbitrarily assumed for 1.1C of ‘zero-feedback’ for +3.7 W/m^2 GHG absorption.

The models are climate models, not climate change models. Thus they have as separate inputs the solar radiation and its dependence on latitude and cloudiness, and the influence GHG’s have on the radiative heat transfer. Changes in the solar radiation are taken into account in a very different way from changes in atmospheric composition.

Yes, I’m sure it’s not forced on the models that these very different changes lead to the same dependence of the response on the single parameter of change in forcing.

There may be some simple models where the response is bound to be exactly the same, but it’s not exactly the same in any large model. How close to the same it is must be calculated by separate model runs.

Citing Pekka: “The models have no separate assumption on that. Depending on their details that either does follow from their other assumptions or that’s not exactly true in a model that considers the changes in more detail taking geographic distribution into account.”

Is it fair to ask how you believe you know this to be the case? While I know the actual physical response itself is modelled different for additional solar than it is for additional GHG absorption (due to a lot of the additional solar going directly to the surface as SW), this doesn’t necessarily mean the ‘instrinc’ effect on raising the surface temperature of each isn’t assumed or comes out to be the same.

It would be easier if you explained how you think a climate model works. Then it would be possible to deal with any misconceptions.

From numerous comments it appears you have some strange ideas about them that I can’t fathom.

Do you recognise them? Probably not, but they aren’t equations that take “no feedback” results and scale them to “feedback results”. They are equations for vorticity, temperature, water vapor concentration, pressure, geopotential.. That’s what GCMs try to do – solve the physics equations for the climate in each “grid cell”.

Note that this climate model has been updated – to version 5 I think, but this is a good place to start.

I understand that the concept of zero-feedback is only theoretical (i.e. doesn’t exist in a real or directly measurable sense). None the less though, it is a measure or calculation of the ‘instrinsic’ effect additional GHG absorption is supposed to have in raising the surface above what it would otherwise be; thus, the significance of its accuracy and absolute correctness is enormous.

The IPCC’s nominal estimate of +3.3C for the equilibrium sensitivity for 2xCO2 is specifically derived from a 1.1C ‘zero-feedback’ baseline, is it not?

Where did you get this idea? From blogs?

See my earlier comment with the link to CAM 3.0.

The relationship is stated as a comparison. It is not derived from, nor calculated from in any way, the ‘no feedback’ result.

So the significance of its (the ‘no feedback’ result) accuracy and absolute correctness is not enormous, it is of minor interest as a calibration point.

please take a look (in CAM 3.0) at pages 117 – 136 for the Parameterization of Longwave radiation, or 102 onwards for Shortwave Radiation – do you see any formulas there for the “no feedback calculation” ?

I think I see your point. However, various studies regarding feedback using satellite data that are purported to show evidence ‘consistent’ with model results are based on the 1.1C ‘zero-feedback’ baseline, are they not?

However, various studies regarding feedback using satellite data that are purported to show evidence ‘consistent’ with model results are based on the 1.1C ‘zero-feedback’ baseline, are they not?

Implicitly they are comparing the results of feedback studies with this value.

Specifically, they are (usually) comparing W/(m2.K) of the measured change compared with the W/(m2.K) of the “no-feedback” change.

And as DeWitt correctly pointed out, technically this isn’t actually a no-feedback change, it is a “Planck feedback” change, which is the increase in W/m2 in TOA OLR for a 1K rise in surface temperature where the surface and atmosphere increase in temperature but the lapse rate stays constant and absolute humidity stays constant rather than relative humidity.

Yes, but to arrive at a final sensitivity estimate from the satellite measurments, they are using 1.1C as the ‘zero-feedback’ baseline. This is the case whether the satellite data is claimed to indicate positive or negative feedback. This is what is being used to ‘validate’ or show results consistent with model derived sensitivity.

The so-called ‘zero-feedback’ Planck response of about 3.3 W/m^2 is itself directly derived from the 1.6 to 1 power densities ratio of the surface and the TOA (i.e. +1C = +5.3 W/m^2, and 5.3/1.6 = 3.3). The 3.3 W/m^2 as a measure indicating ‘no-feedback’ is not the issue.

Yes, but to arrive at a final sensitivity estimate from the satellite measurments, they are using 1.1C as the ‘zero-feedback’ baseline. This is the case whether the satellite data is claimed to indicate positive or negative feedback. This is what is being used to ‘validate’ or show results consistent with model derived sensitivity.

No. The satellite data is compared with the model data. As a matter of interest the “zero feedback” baseline is shown.

If it wasn’t used, wasn’t cared about and wasn’t even known the papers would have the same results in them. You don’t need it to produce a W/m2.K value from a model. You don’t need it to produce a W/m2.K value from TOA satellite measurements.

Often the papers decompose the model feedback into various components (done by removing bits of physics from the model, or holding certain variables constant while letting other components change).

Also, is is fair to ask if there a paper in the literature that effectively serves as “Proof that all of absorption acts to ultimately warm the surface”. I’ve looked and haven’t found anything that really addresses this issue.

Added absorption by GHG’s leads to less outgoing radiation. That’s seen very clearly in the calculations presented in the recent long series of posts.

Reduced OLR means that more energy is retained by the Earth system. The heat capacity of the atmosphere is so small that it cannot take much of that. For the remaining part the only possibility is that it warms the surface.

Yes, but the claim is 100% of the absorbed GHG flux acts to ultimately warm the surface (the same as post albedo solar power). Given the atmosphere radiates its absorbed energy both up and down, and the absorbed energy has the potential to leave the atmosphere over twice the area (i.e. either to the surface or out into space), it seems to be an arbitrary and dubious claim.

The primary way energy is transferred from the atmosphere to the surface is by radiation, right? And specifically not via some sort of conduction process, right?

The surface at 288K is supplied with a net energy flow of about 390 W/m^2 with only 240 W/m^2 entering the system from the Sun. The difference is +150 W/m^2 of energy supply to the surface. Are you saying the 150 W/m^2 is a quantification of total GHG absorption?

Yes, the energy is retained, but only temporarily. It does not stay put otherwise the energy in the atmosphere would be monotonically increasing, but it’s clearly not. This means all the energy entering the atmosphere is eventually coming out, and for which there are two potential ways out – either to the surface or out into space.

The ‘consensus’ claim is +3.7 W/m^2 of GHG absorption has the exact same ability to act to ultimately warm the surface the same as +3.7 W/m^2 post albedo solar power, right? This is why both are claimed to have a ‘zero-feedback’ response at the surface of 1.1C, is it not?

If this is true, it should – like anything else, require proving it, right? I think it is highly dubious given the post albedo solar flux is the only significant source of energy and is continuously downward radiated in (all in the direction toward the surface), where as the absorbed GHG flux has equal potential to be radiated back up as it does down.

An easy way of proving that 100% of GHG absorption is equal to post albedo solar forcing would be for an amount equal to the total absorbed GHG flux to be the exact difference in net energy supplied to the surface in the steady-state to that of the post albedo solar flux entering the system. If not, then what is the proof?

You mean most of the accumulated energy in the system is stored in the oceans? I certainly agree with that; however, this doesn’t seem relevant to whether watts of GHG absorption are equal to watts of solar forcing in their ability to act to ultimately warm the surface. For the energy to be stored below the surface it has to ultimately reach the surface first as part of the net flow of energy supplied to the surface, and not all the energy entering the atmosphere, including the absorbed GHG flux, ultimately flows to the surface, as a significant amount of it ultimately flows away from the surface and out into space.

The net energy flow at the surface is zero at steady state. The gross flow into the surface isn’t ~390 W/m², it’s ~492 W/m², ~333 W/m² of LW radiation from the atmosphere and ~161 W/m² of SW solar radiation. The gross flow out is also ~492 W/m², ~390 W/m² by radiation and ~102W/m² by convection. Your failure to grasp the concept that convective energy transfer can be one way is the source of all your problems. Both radiative and convective energy are thermalized when absorbed into the atmosphere. Once that happens, it doesn’t matter where the energy came from.

A state of energy balance at the surface occurs when energy gain equals energy loss. This doesn’t mean there isn’t a net energy supply to the surface, or that the net energy supply to the surface is zero.

The key point is, for a state of energy balance (for 288K), all power in excess of 390 W/m^2 incident on the surface has to be exactly offset by power in excess of 390 W/m^2 leaving the surface, and that the surface specifically emits 390 W/m^2 of radiative power solely due to its temperature (and emissivity, which is really close to 1). Moreover, any non-radiative power leaving the surface has to be in excess of that directly radiated from the surface, otherwise the surface temperature would be higher, where as there is no such requirement for the proportions of radiative and non-radiative power incident on the surface from the atmosphere. Thus, the net energy (i.e. power) supplied to surface cannot be more (or less) than about 390 W/m^2 to sustain 288K.

The key point is, for a state of energy balance (for 288K), all power in excess of 390 W/m^2 incident on the surface has to be exactly offset by power in excess of 390 W/m^2 leaving the surface…

Correct. The excess power entering the surface that isn’t radiated leaves by convection.

Thus, the net energy (i.e. power) supplied to surface cannot be more (or less) than about 390 W/m^2 to sustain 288K.

Wrong. Your hand-waving amounts to saying 2+2 = 3. Downwelling LW is measurable as is downwelling solar SW. The sum is greater than the upwelling LW from the surface and greater than the measurement error.

In a convection oven, does a piece of meat roast faster when the fan is on then when it isn’t? Of course it does. It’s about equivalent to raising the oven temperature by 25C. Convection does transfer net energy from the surface to the atmosphere, specifically ~102 W/m².

All I’m saying is the additive superposition principle must apply to the effects of energy (and power) on the surface temperature. I apologize if I’m not using the exact correct phrasing to describe this.

To the extent that the surface receives more direct radiative power from the atmosphere and Sun that it emits, much of this direct radiative flux is constantly replacing kinetic (non-radiant) energy leaving the surface but not returned as kinetic, effectively making it net zero energy flux entering the surface (i.e. energy circulating within the system or circulating within the surface and TOA boundaries)

This doesn’t mean there is not a large cross exchange between radiant power from the surface and non-radiant power from the surface, where a significant portion of the energy which left the surface non-radiatively finds its way radiated out into space, accelerating the transport of energy from the surface to the TOA, and thus making the surface cooler than it would otherwise be.

In fact, if we use Trenberth’s numbers, they show what I’m saying is true. He has a net non-radiative loss from the surface to the atmosphere of 102 W/m^2 and 324 W/m^2 directly radiated from the atmosphere to the surface. If you subtract 102 W/m^2 from 324, you’re left with 222 W/m^2, and 222 + 168 directly from the Sun as SW = 390 W/m^2, which equals the net energy supplied to the surface to sustain 288K (and also the amount radiated from the surface into the atmosphere).

In effect, 102 W/m^2 of the 324 W/m^2 is the replenishing the 102 of non-radiant flux leaving the surface but not returned, making it a net zero energy flux entering the surface.

If you subtract 102 W/m^2 from 324, you’re left with 222 W/m^2, and 222 + 168 directly from the Sun as SW = 390 W/m^2, which equals the net energy supplied to the surface to sustain 288K (and also the amount radiated from the surface into the atmosphere).

And if you subtract 390 from 324 + 168 you get 102. If you subtract 390 + 102 from 324 + 168 you get zero. Energy in equals energy out. This isn’t news, except possibly to you. But you do seem close to admitting that the KT97 and TFK09 energy balance at the surface adds up with no double counting or other tricks.

Is net energy supply to the surface not a legitimate scientific concept?

Sure, if you define it correctly. But you don’t. The total power supplied to the surface is 492 W/m², 168 W/m² SW + 324 W/m² LW. You don’t get to arbitrarily subtract only convective power emitted by the surface from that amount and claim the real net power is only 390 W/m². If you’re going to subtract emitted power, you have to subtract all the emitted power, both radiative and convective. Then you end with a net of nearly zero.

The only real net is the imbalance, i.e. around 1 W/m^2. With all others we end up in endless semantic discourse.

The other reasonable alternative is to define precisely what we are talking about and to be sure that the definition is understood by everyone participating in the interchange. On the web we can seldom be sure of that.

“Essentially the whole imbalance will reach the surface whatever the reason of the imbalance. As atmosphere cannot take much of it there are no other alternatives.”

What do you mean there are no alternatives? A substantial portion of the energy flow into the atmosphere is ultimately directed out into space as part of the LW flux leaving at the TOA. In fact, the potential area for the energy to leave at TOA is slightly larger than the area of the surface because the Earth is a sphere.

You appear to be saying that all the energy absorbed GHGs (or an amount equal to it) only exits the atmosphere by going to the surface and none of it exits the atmosphere by going out the TOA into space. Or that effectively the energy absorbed GHGs never leaves the system and all returns to the surface. Being that a huge portion of the LW flux that exits at the TOA originates from the atmosphere as opposed to the surface, this can’t be right.

BTW, does anyone know what the total GHG absorption is on global average? That would be an important figure to know here. If it is substantially more than 150 W/m^2, then I don’t see how additional GHG absorption can be considered equal to post albedo solar power in its ability to act to ultimately warm the surface.

I agree there is an imbalance which will require the atmosphere and ultimately the surface to warm in order to re-establish equilibrium with space, but I fail to see how this in and of itself somehow equates watts of GHG absorption to watts of post albedo solar energy in their ability to act to ultimately warm the surface.

Do you agree that the energy absorbed by GHGs has the potential to be re-radiated back up away from the surface, and that energy radiated up in the atmosphere is part of the radiative cooling process of the system (i.e. in the act of cooling and not warming)? Do you agree that post albedo solar power is all dowwnard radiated in and continuously acting to warm (i.e. all flowing in the direction towards the surface)?

So net energy supply to the surface to sustain 288K is not 390 W/m^2? You’re actually claiming this?

And once you have grasped this essential basic principle you will be past day 1 (not week 1 or month 1) of heat transfer. The fact that you demonstrate incredulity on this point means you have not yet passed day 1.

If you can appreciate that you haven’t passed day 1, it will be the first step to a wonderful future.

How much time have you spent writing comments just on this blog? Honestly, the best way to learn basics is to read a textbook and try to understand the worked examples. (Or even try to understand the comments on this blog rather than explaining why everyone who understands heat transfer is wrong. Please)

Net energy supply to a body, Enet, to sustain temperature, Tx?

…. Enet = 0

That is the definition of “sustain” which I take to mean “steady state”. And so regardless of the temperature of that body, if it is in steady state it is zero. This is the first law of thermodynamics. And of course, Enet=Ein-Eout.

For a body (with an emissivity of 1.0) to be at Tx=288K, what value of Ein do we expect?

Don’t worry about the surface. It’s temperature will always be determined mainly by the combination of ocean heat content and the energy balance at TOA. I.e. by the amount of energy already stored and by the imbalance that adds to the energy content. The ocean temperature sets the reference point and the larger the imbalance the more the surface temperature will differ from that of deeper ocean.

The details may be difficult to determine, but that doesn’t matter.

The imbalance can be determined and understood more easily at TOA than at surface.

If surface temperature is to increase by 1.1C (from 288K to 289.1K), for example, it has to receive more energy (i.e. more power), right? How is this increase in energy supply quantified? That is, how much additional energy supply is required to raise the surface temperature 1.1C?

I say it’s about an additional 6 W/m^2, which then for the requirement to sustain 289.1K, all power in excess of 396 W/m^2 incident on the surface has to be exactly offset by power in excess of 396 W/m^2 leaving the surface. And so on and so forth depending on the temperature or temperature change.

You’re saying there is no way to express the required 396 W/m^2 quantity for 289.1K? This is how I’m interpreting SoD’s and your comments.

So then the concept of ‘net energy supply’, as I’m using it, when additive superposition is at work, is not valid?

That’s correct. Your understanding of the terms “net” and “additive superposition” mean something different than everybody else. For example:

So the surface is supplied with a net energy of zero in the steady-state?[my emphasis]

The use of net in that sentence is incorrect and nobody ever said that. The power supplied to the surface is 492 W/m², there is no net except in your mind because you apparently think that energy transfer by convection is somehow so different from radiative energy transfer that it can’t be mentioned in the same sentence. OTOH, the net energy balance at the surface is most likely less than 1 W/m² .

You’re actually claiming this?

Straw man much. Besides, you’re the one making claims that differ from reality.

Then how is increase in energy supply to the surface to raise the surface temperature quantified? I assume you agree that for the surface to warm it has to receive an increase in energy supply (i.e. more power).

For that the surface must have an energy balance that allows it to emit more IR without cooling.

Everything else than the emitted IR must increase for that.

The above sentence should be well defined and tell, what’s needed. Why don’t you accept that.

Then you may continue to figure out what the “everything else” includes. When you do that, you will find out that some contributions are easier to determine empirically than others. Finally the most difficult part is estimated from the requirement that the overall balance is known much more accurately. Convection is probably the ultimate component that cannot be estimated in any other way as accurately than the others. Down-welling radiation (both solar SW and LWIR) is easier to measure and latent heat transfer can be estimated from the total amount of rain, which is measurable, convection is very difficult to measure directly.

Then how is increase in energy supply to the surface to raise the surface temperature quantified?

Using models, of course. The model complexity varies from radiative transfer only models like MODTRAN to one-dimensional radiative/convective models like the one SoD wrote to full bore coupled air/ocean general circulation models (AOGCM). Notice I didn’t include a single slab gray atmosphere model. How well these work isn’t known yet. The AOGCM’s currently appear to be biased high in their estimates of the trend in surface temperature. But they all agree that increasing CO2 over time will also cause the surface temperature to increase. It’s also clear even from MODTRAN that you can’t assume that convective energy transfer won’t be affected by increased surface temperature. Downwelling LW from the atmosphere increases faster than upwelling LW from the surface with temperature at constant lapse rate. That implies that convective energy transfer will increase to make up the difference.

There are effectively two flows of energy entering and leaving the surface. One is flowing surface -> atmosphere -> surface, where as the other is flowing Sun -> space -> atmosphere -> surface -> atmosphere -> space. Only the latter flow of energy is adding energy to the surface to sustain or modulate the surface temperature. The former flow of energy is that which is circulating within the system (i.e. circulating within the surface and TOA boundaries).

What I’m trying to say is the energy (i.e. power) added to the surface from the latter flow of energy is only about 390 W/m^2 to sustain 288K. This is what I mean by ‘net energy supply’ to the surface being about 390 W/m^2.

My question is, if referring to this as ‘net energy supply’ is not correct, what is the proper or official name (or phrase) that correctly referrs to this quantity?

(*Of course there are an infinite number of ways the quantity can be manifested at the surface – I know that)

Yes, but what is the quantity (power density) that designates the temperature from which an increase or decrease in temperature from a change in Enet would occur? Is this quantity not about 390 W/m^2 for 288K? That is, for the temperature to increase above 288K, this quantity would have to increase above 390 W/m^2 and for the temperature to decrease, this quantity would have to decrease below 390 W/m^2.

How is the quantity of 390 W/m^2 to sustain 288K, independent of how it’s ultimately manifested at the surface, properly designated or referred to?

You should finally accept that the causality works in the opposite direction. Other factors determine the surface temperature and the convection settles at a value that’s required by the balance at that temperature.

The other factors that determine the temperature include most importantly the energy balance at TOA and the lapse rate. The energy content of the oceans has also a role in that.

For this reason it’s pointless to ask, how the energy flows at the surface determine the temperature (they don’t).

The flow of energy in and out of the surface that’s going Sun -> space -> atmosphere -> surface -> atmosphere -> space (i.e. in and out of the whole system) requires a power density of about 390 W/m^2 to sustain 288K. This can be manifested in an infinite number of ways with an infinite number of gross incident on and leaving power at the surface, but for 288K, in every case, each must always been in excess of 390 W/m^2.

“You should finally accept that the causality works in the opposite direction. Other factors determine the surface temperature and the convection settles at a value that’s required by the balance at that temperature.”

Yes, this is obvious and I agree completely. But I fail to see how this is related to the issue in contention here.

If the surface is to receive more direct radiative power from the atmosphere (as a result of GHG warming of the atmosphere), this will not necessarily raise the equilibrium temperature of the surface. It’s at least theoretically possible that the increase in direct radiative flux could be exactly offset by and equal and opposite increase in convective flux leaving the surface. In this case, the total incident on and leaving power at the surface will increase, but the surface temperature would remain the same. How then do we quantify the increase in energy supply to the surface required to raise the surface temperature? That is, how do we quantify the increase in energy supply required to raise the surface temperature above 288K?

It’s at least theoretically possible that the increase in direct radiative flux could be exactly offset by and equal and opposite increase in convective flux leaving the surface.

Nope. If any new imbalance were to go 100% into convection, then there’s no reason that convection wouldn’t increase without an imbalance and the current surface temperature would be lower than it is now. That could only be true in a thought experiment and it’s pretty clear that it would fail the reasonableness test. At best, variations in the ratio of convective to radiative energy transfer from the surface contribute to weather noise.

Let’s say from a starting temperature of 288K the direct radiative power from the atmosphere to the surface increased by 10 W/m^2 and the convetive flux leaving the surface increased by 4 W/m^2, resulting in new equilibrium surface temperature. What is the new equilibrium surface temperature and how is this known?

From a starting temperature of 278K, if the direct radiative power from the atmosphere to the surface increased by 10 W/m^2 and the convective flux leaving the surface increased by 4 W/m^2, resulting in new equilibrium surface temperature – what is the new equilibrium surface temperature?

The answer is about +1.5K, where as in the first example the answer is about +1.1K. In both cases it’s +6 W/m^2 in net energy gained, right? How can it be known that in the first example it results in +1.1K if 390 W/m^2 is not the baseline from which the +6 W/m^2 is added to?

You are correct in your first answer (assuming surface emissivity = 1.0 and some assumptions about timing)
You are incorrect in your second answer.

In both cases we solve an equation for energy balance using a) the first law of thermodynamics b) the Stefan-Boltzmann equation c) prescribed boundary conditions.

This principle is the same for more complex problems, sometimes the result is a set of simultaneous equations, sometimes the result can only be found iteratively or via numerical methods (like matrix inversion or forming a “3-d mesh” and solving with a finite element program).

a) If we gloss over some details and say, somehow we know at the new steady state that the change in convective energy = -4 W/m2:

Eout(radiative)’ – Eout(radiative) = 10-4 = 6

=> σTs’4 – σTs4 = 6

=> Ts’ = (6/σ + Ts4)1/4

=> Ts’ = 289.1 K

b) For the second case, Ts=278K, with similar assumptions:

Ts’ = 279.2 K
= (6/σ + 2784)1/4

c) For both cases if we found that at the instant of change:

ΔEin(radiative) = +10 W/m2
ΔEin(convective) = -4 W/m2

then we would need an equation of convective heat transfer to determine the new steady state temperature, Ts’.

Hopefully this last point c) makes sense.

Then you asked:

How can it be known that in the first example it results in +1.1K if 390 W/m^2 is not the baseline from which the +6 W/m^2 is added to?

I’m not quite sure I understand the question.

We solve an equation, the same equation in both cases, and out comes the number. Obviously the answer is different in both cases because it is not a linear equation (it is a function of T4)

If instead we knew that:

i) the atmospheric temperature had changed to Ta’
ii) the convective energy transfer instantaneously reduced by 4 W/m2
iii) convective energy transfer was governed by equation, Ec = h.U(Ts-Ta), where h was a constant for a given density, surface roughness and specific heat capacity and U was wind speed at a reference height

The whole point is temperature of slaved to power via the S-B law, and the T^4 relationship between temperature and power is non-linear. That is, the warmer the starting temperature, the greater amount of net power gained is required to effect and sustain an equal increase in temperature.

For example, +1.1K from 288K requires an increase in net energy gained greater than +1.1K from 278K. This is the case regardess of how the net energy gained is manifested at the surface.

BTW, the second calculation I did was done quickly and relatively roughly. It may be more like about +1.4K. None the less, all I’m doing is adding the +6 W/m^2 to the pure black body power baseline of the original temperature and then converting back to temperature.

The reason why this works for the surface of the Earth, for a state of energy balance, is because the entire energy supply to the system is all EM radiation (excluding an infinitesimal amount from geothermal), the surface radiates the same amount of (net) power it is supplied, the overwhelming amount of energy in the system is stored below the surface (more than 99.999%), and EM radiation is all than can pass across the system’s boundary between the atmosphere and space. If there were a significant energy supply, from say geothermal, it wouldn’t work, or if a significant amount of the energy in the system was stored in the atmosphere it also wouldn’t work (i.e. wouldn’t provide the correct answer)

“then we would need an equation of convective heat transfer to determine the new steady state temperature, Ts’.

Hopefully this last point c) makes sense.”

No, it doesn’t make sense to me. I’m assuming in both cases a new steady-state has been arrived at with +6 W/m^2 in net energy gained (+10 W/m^2 of radiation and -4 W/m^2 of convection). Morover, if I know the new steady-state temperature, I can deduce the amount of net energy gained required to effect and sustain it, independent of how it’s actually manifested at the surface. For example, I can deduce that +3C from baseline of 288K requires +16.6 W/m^2 of net energy gain, from which I can further deduce will result in +16.6 W/m^2 radiated from the surface.

This is why quantifying sensitivity using the dimentionless ratio of the surface and TOA (radiative) power densities, as GW does, is valid and works (i.e. gets the same answer). For example, +3C from a post albedo equivalent forcing of 3.7 W/m^2 requires a dimentionless gain of 4.5 (16.6/3.7 = 4.5). +1.1C from a forcing of 3.7 W/m^2 requires a gain of about 1.6 (6/3.7 = 1.62, which is the same as the global, absolute, or so-called ‘zero-feedback’ gain of the system (390/240 = 1.62).

The main point is adding the +6 W/m^2 to the 390 W/m^2 baseline for 288K still provides the same (correct) answer. That is, +1.1K (and will always be the case regardless of how the +6 is manifested). Such is the entire point of an ‘equivalent’ model or equivalent systems analysis. It’s not modelling the actual behavior, yet still arrives at the correct answer (i.e. the final calculated surface temperature change is the same).

Or just the same as if the additional 6 W/m^2 arrived at the surface solely as direct radiative power from the atmosphere (as would be the case for a pure black body where convective flux ‘K’ is equal to zero).

By the term ‘net energy flow’ at the surface, I’ve always meant ‘net power gained’ at the surface, and that for 287K, ‘net power gained’ cannot be more or less than about 385 W/m^2 to sustain 287K. If more than 385 W/m^2 is gained, the surface warms, and if less than 385 W/m^2 is gained, the surface cools. And that this is entirely independent of how the joules arrive to the surface.

I guess no one is interested in this. I think I’ve finally found the right language to describe what I’ve been trying to say for so long now. Anyway, my understanding (at least) is the 146 W/m^2 in GW’s div2 is the additional amount of net power gained at the surface that is not supplied into the system by the Sun. Since the atmosphere creates no energy of its own, it has to have its ultimate origin in radiative resistance to cooling via GHGs and clouds (i.e. the absorption of upwelling radiation acting to cool that is absorbed and subsequently re-radiated back downward). Since the difference of 146 W/m^2 is not a quantification of global average GHG absorption, incremental absorption is not equal to incremental post albedo solar forcing and must be less. That it turns out to be about half shouldn’t be surprising given the probability of a photon emission anywhere in atmosphere is always 50/50 up or down and all the energy that enters the atmosphere has two potential exit paths (either to the surface or out into space).

Also, GW references the following graph of 25 years worth of ISCCP satellite data in support of his so-called ‘equivalent model’:

If I’m interpreting this correctly, I believe what it is showing is that even if 100% of the radiative power flux emitted from the surface is absorbed by the atmosphere (i.e. by clouds, which are nearly if not entirely opaque to upwelling IR from the surface), and amount equal to at least 1/2 of the surface radiative power is being emitted from the cloud tops toward space, matching or showing consistency with the equivalent model (i.e. that the radiative power emitted by clouds relative to the radiative power emitted by the surface is never less than 1/2).

At any rate, I can see no one is interested in this. I did make GW aware of the discussion here early on in the thread, but I suspect he’s been too busy at work to respond or get involved in the discussion. Perhaps at some point he will come and explain first hand all of these things (and much better than I have). I’d definitely be willing to dismiss his analysis if he was claiming the 3.7 W/m^2 was all that of surface radiative power newly absorbed, but he’s not and never was (that was entirely my error and misintepretation), so perhaps he still has a valid case.

I’ve spent quite a bit more time thinking about this, and I think I understand at least what George White is doing and claiming. Basically, the ‘T’ input of 0.241 to the simplified ‘equivalent’ model is specifically that taken from the real atmosphere (i.e. the real system). That is, it’s taken from a multi-layered radiative transfer model of the real atmosphere that accounts for changes in both upwelling and downwelling radiation through the whole atmosphere, for which the calculated 3.7 W/m^2 per CO2 doubling is the increase in upwelling LW radiation absorbed by the atmosphere (i.e. the decrease in ‘T’ and the increase in ‘A’). I believe this is fundamentally what makes the simplified model ‘equivalent’ to the real atmosphere. That is, in the steady-state, each is constrained by the same boundary conditions from the same ‘T’ input.

Now in addition to this, my understanding of the way +1.1C of so-called ‘zero-feedback’ at the surface is arrived at for +3.7 W/m^2 of post albedo solar power is to take the dimentionless ratio of the surface and TOA power densities, which is 1.61 (385/239 = 1.61, where at 287K the surface is supplied with net of about 385 W/m^2 and 239 W/m^2 is the post albedo solar power entering the system and the LW flux exiting the system at the TOA), and then multiply it by the 3.7 W/m^2 and then add the result back to the baseline of 385 W/m^2 and convert back to temperature. That is, 1.61 x 3.7 W/m^2 = 6.0 W/m^2, and 385 W/m^2 + 6.0 W/m^2 = 391 W/m^2 = 288.1K (or +1.1C). (*I believe this is really all Arrhenius and other formulations are doing).

To arrive at 1.1C for +3.7 W/m^2 of incremental GHG absorption they are effectively using the same power densities ratio of 1.6 between the surface and TOA and making the same calculation, which is arbitrary not really valid because:

1. Energy re-emitted by GHGs, either directly or by transfer to the atmosphere (and subsequently emitted by the atmosphere), is not an energy source to the system (it is only energy re-directed from that supplied into the system by the Sun).

2. The energy absorbed by GHGs is subsequently re-radiated both up and down (i.e. both away from the surface and toward the surface).

3. Post albedo solar forcing is not only an energy source, but all in the act of radiating downward. That is, post albedo solar power is a continuous stream of downward radiated energy flowing into the whole Earth-atmosphere system, all in the direction toward the surface (i.e. all continuously acting to warm), where as the power absorbed and re-radiated by GHGs and the atmosphere is not. (*I assume it is agreed that radiation emitted up in the atmosphere is in the act of cooling or part of the radiative cooling process of the system)

4. The fundamental mechanism for how GHGs elevate the surface temperature above what it would be in their absence is the absorption of upwelling radiation acting to cool that is absorbed and subsequently re-radiated back downwards, thereby increasing radiative resistance to cooling; and specifically not via some sort of conduction process. Every description or definition of the GHE, including that from the IPCC, uses phrasing very similar to this one from Wikipedia:

“The greenhouse effect is a process by which thermal radiation from a planetary surface is absorbed by atmospheric greenhouse gases, and is re-radiated in all directions. Since part of this re-radiation is back towards the surface and the lower atmosphere, it results in an elevation of the average surface temperature above what it would be in the absence of the gases.”

Thus incremental GHG absorption would not be equal to incremental GHG ‘forcing’ or incremental post albedo solar forcing as claimed and should be less (and like anything else in engineering and physics, requires quantification). I believe that fundamentally what George is doing is making this quantification by calculating the equivalent fraction of the flux absorbed by GHGs (and clouds) that exits the planet from the atmosphere, and which turns out to be about half.

(*BTW, I believe all he’s trying to show with the simplified ‘equivalent’ model is that the net flow of energy in between the boundaries would be the same as if half of the flux absorbed by atmosphere is ultimately radiated to space, never to be supplied to the surface. That is, the surface would be supplied with the same amount of joules and same amount of joules would enter and leave the system from the Sun. And that’s it – nothing more).

______________________________________

I think a lot of what George is doing is being fundamentally misunderstood because in the real system the balance at the surface is the sum of a radiant and non-radiant flux where additive superposition applies to the effects of energy (and power) on the surface temperature. To the extent that the surface receives more direct radiative power from the atmosphere and Sun than it emits, the excess must be replacing non-radiative power leaving the surface, but not returned (i.e. making it net zero energy flux entering the surface, or energy that is circulating within the surface and TOA boundaries).

A critical point is, in the steady-state, all power in excess of 385 W/m^2 incident on the surface has to be exactly offset by power in excess of 385 W/m^2 leaving the surface, and that the surface specifically emits 385 W/m^2 of radiative power solely due to its temperature (and emissivity, which is really close to 1). Moreover, all non-radiative power leaving the surface has to be in excess of that directly radiated from the surface, otherwise the surface temperature would be higher, where as there is no such requirement for the proportions of radiant and non-radiant power incident on the surface from the atmosphere. I believe George is just claiming that 385 W/m^2 is the net power gained at the surface required to sustain 287K, which is then also the power directly radiated from the surface.

I believe this is all he means when he says:

“At the bottom boundary, the surface at 287°K radiates 385 W/m², which must be replaced with the same amount of power entering the surface from the bottom of the atmosphere.”

____________________________________________

The biggest and most ubiquitous objection seems to be that everyone doesn’t think George is accounting for the huge amount of non-radiative flux that leaves the surface (much of which doesn’t return). I think part of the disconnect arises because George has a different meaning for the term ‘radiative balance’ than how it is used in atmospheric science. I believe by the ‘radiative balance’ he means the photon energy balance of the planet (i.e. the entire energy budget of the system is all photons or all EM radiation). The system in a state of energy balance, independent of how the balance is manifested (at the surface or anywhere else), is what he means by ‘radiative balance’.

While George is only considering EM radiation for the ‘equivalent’ model, this doesn’t mean there is not a large cross exchange between radiant power from the surface and non-radiant power from the surface, where a significant amount of that which leaves the surface non-radiatively finds its way radiated to space. He’s just saying that in the steady-state, it must result in an equal and opposite amount of surface radiative power absorbed by the atmosphere but not exiting to space (i.e. finding its way back to the surface some how in some form). Or just that such an exchange from non-EM to EM must be offset by an equal and opposite exchange from EM to non-EM (*otherwise, in the steady-state, COE would not be satisfied). I believe this is what he means where he says in the fourth paragraph:

“A further constraint of Conservation Of Energy is that the global net non radiative flux between the atmosphere and the surface must be zero in the steady state if the radiative flux is also zero. While radiative flux to and from the surface can be traded off against non radiative flux, it makes no difference to the overall radiative balance.” (i.e. it makes no difference to the calculation and resulting value of ‘F’ – not that it makes no difference to why the surface energy balance is what it is).

(*Also, I believe the reason why it is valid to consider only EM radiation for the ‘equilvalent’ model is because, excluding an infinitesimal amount from geothermal, the entire energy supply to the system is all EM radiation, and EM radiation is all that can pass across the system’s boundary between the atmosphere and space; and because the surface is so close to a black body, it specifically radiates the same amount of power it is ultimately supplied as a result of all the physical processes in the system – both radiative and non-radiative).

____________________________________________

One final point:

That everyone sees George as claiming some radical new (and erroneous) knowledge about the physics of the atmosphere and I see what he’s doing as basic and fundamental (i.e. a basic and required physics and engineering exercise), is what tells me something here is being grossly misunderstood. If George is right it would be more the correction of an oversight – not any new knowledge about the physics of the atmosphere. That is, unless the atmosphere being limited to about 50% opacity is thought to be radical new knowledge, as I certainly don’t think it is (and I don’t think George does either).

One other point is it’s my understanding that the IPCC and climate science community claims that in the absence of feedback, +1.1C is the required amount needed to get rid of the -3.7 W/m^2 at TOA, and not that +1.1C is an amount that would get rid of the imbalance. This would seem to be an important distinction, because I agree that if surface temperature were raised by 1.1C, independent of how it were raised, it would get rid of the imbalance; however, this seems trivial and in no way means it would be the required amount for incremental GHG absorption.

I believe George’s fundamental claim is that what climate science designates as ‘zero-feedback’ is really only half of the net absorption increase or only half of incremental GHG absorption.

That is, the context of the div2 analysis is largely that of so-called ‘zero-feedback’, which assumes the complexity or average net behavior of the complexity of all the physics of the atmosphere will not change upon a change in the energy balance, like when CO2 is doubled. So in order to calculate so-called ‘zero-feedback’, using George’s model, one needs to multiply the post albedo solar or equivalent forcing (in this case 2xCO2) by the post albedo gain of the system (385/239 = 1.61; 3.7 W/m^2 x 1.61 = 6.0 W/m^2 = 1.1C from a baseline of 287K). That is, +3.7 W/m^2 of post albedo solar power has a ‘zero-feedback’ warming of about 1.1C (as illustrated prior above), and +3.7 W/m^2 of GHG absorption, such as that which occurs from 2xCO2, would have a ‘zero-feedback’ warming of only about half or 0.55C (‘F’=0.5, so 3.7 W/m^2*0.5 = 1.85 W/m^2; 1.85 W/m^2 x 1.61 = 3.0 W/m^2 = 0.55C).

Another thing regarding George’s div2 that I don’t think had been mentioned is that non-radiative energy flux from the the surface to the atmosphere generally makes the surface cooler than it would otherwise be – not warmer (at least as a 1st order effect), because it accelerates the transport of energy from the surface to space. This is accomplished by the energy being moved non-radiatively to higher parts of the atmosphere, where when radiated, has a greater chance of passing through the remaining atmosphere into space, right?

This is why I don’t understand why the amount of non-radiative flux that leaves the surface and doesn’t return matters relative to what George White is doing and trying to show. The elevation of the surface temperature above what it would otherwise be is fundamentally a radiative resistance effect, right? It seems to me that the bottom line is, in the steady-state, every joule that goes into the atmsophere, whether initially radiant or non-radiant, must come out, and there are only two ways out – either to the surface or out into space. Otherwise, the energy stored in the atmosphere would be monotonically increasing, which I think we all agree is not the case.

I think George is just saying and/or claiming that all of the non-radiative flux that leaves the surface (as well as returns) really only involves how the surface ultimately gains about 385 W/m^2 to sustain 287K. Moreover, the energy contained in the atmosphere is an infinitesimal fraction of that contained below the surface and only persists in the atmosphere for a very short amount of time. That is, it’s not significant relative to the surface’s long term steady-state average.